Soliton, one of the core problems of nonlinear science, can be traced back to the isolated waves discovered by Russell, a British national electric power scientist, in 1834. Later, Dutch mathematicians Korfeweg and Vries studied it in 1895 and got the now famous KDV equation. It was not until 1965 that Kruscher defined it as a soliton. During this period, the most significant applications are laser aiming and optical fiber communication. The former explained some previously unexplained physical phenomena, while the latter brought about a revolution in the media.
As the core problem of nonlinear science, soliton has the following characteristics: first, soliton solution; The second is the Bach Lund Exchange; Third, the law of infinite conservation; The fourth is the scattering inversion method. It is these characteristics that make soliton a hot issue in the world today.
Summarize its latest research progress, one is peah Solifon, such as Camassu-Holm equation; The second is the integrability of three-dimensional Eulv equation.
Excerpt from Academician Guo Bailing's academic report on nonlinear science.
Early history
Scott Russell was the first person to discuss this problem. He gave the British Association for the Advancement of Science
The report was published in 1845.
About fluctuation
A report on fluctuations. Scott Russell, gentleman, Master of Arts from the Royal Society of Edinburgh.
Membership, made at the annual meetings of 1842 and 1843.
committee member
Sir john robinson, Secretary of the Royal Society of Edinburgh.
Scott Russell, a gentleman, is a member of Edinburgh Royal Society.
I believe I'd better introduce this point by describing the first time I met him in person.
Phenomenon. I was watching a pony pull forward quickly along a narrow waterway.
The motion of the ship. When the ship stopped suddenly, a lot of water was pushed by the ship and disappeared in the waterway.
Stop, the water is piled up in front of the bow and excited violently, and then the water wave suddenly presents a large area.
The isolated bulge is a round, smooth and well-defined water pile. It's huge.
The speed rolled forward, leaving the boat behind. Water continues to flow along the waterway.
Has obviously changed its shape or reduced its speed. I rode after it and caught up with it, but it was still safe.
Keep its original shape about 30 feet long, 1 foot to 1 foot and a half high, about once an hour.
Roll forward at 8 or 9 miles. Gradually, its height dropped. When I chased a mile or two,
Then disappear at the bend of the waterway. So, in August of 1834, this is the first time I have it.
Have the opportunity to see such a unique and beautiful phenomenon. I call this phenomenon translational wave.
This name is now widely accepted by people. This phenomenon has been almost the same since I found it.
It is an important part of each fluid resistance; And the ocean belongs to this kind of wave.
The huge uplift, coupled with the rhythm of the earth, makes our river rise and stay on our coast.
Scroll.
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After that, Scott Russell went on to suggest that the isolated body he met actually represented fluid mechanics.
A wide range of solutions. He first called it "translational wave" and later called it "solitary wave".
Unlike shock waves, shock waves are strange on the wavefront, while "solitary waves" are regular everywhere.
There is no singularity. Solitary waves are stable and will not disperse, so they are different from any waves composed of ordinary planes.
Wave packets composed of wave solutions are different. However, Scott Russell can't satisfy all his colleagues.
Everyone believes it. As can be seen from Figure 7.2 (from the article by Lord Rayleigh 1876),
The problem of solitary waves was still a heated debate among major physicists at that time.
This argument was not resolved until 1895, when Kotwich and Desfray were based on the following.
Solutions of nonlinear hydrodynamic equations Kotwich and Devrey equations (now called isolation)
Sub-solution) gives a comprehensive analysis. However, the remaining problem is this stability,
In addition to physical fluid mechanics, nonsingular non-dispersive solutions can also appear in other fields. through
After the work of Fermi, basta and ulam in the early 1950s, this problem was further advanced.
Using Maniac I, one of the largest computers, they studied the energy trend average of 64 harmonic oscillators.
In the process of uniform distribution, there is weak nonlinear coupling between these harmonic oscillators. initial
All the energy is concentrated on a harmonic oscillator. They were surprised to find that this is usually about
The concept of how to achieve thermal balance is very wrong.
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London, Edinburgh and Dublin
Philosophical journals and scientific journals
[Episode 5]
65438+April 0876
Thirty-two Lord Rayleigh, Master of Arts, Fellow of the Royal Society.
……
Solitary wave
This is Scott Russell's name for a special wave. This wave is not listed in 1844.
It is described in the report of the association.
……
Airy's paper on tides and waves may still be the most authoritative argument. He seems to be
I didn't realize there was anything unusual about Solitary Wave.
……
On the other hand, Professor Stokes said, "Mr. Russell's view is that solitary waves are a special phenomenon.
This is by no means inferred from the environment in which waves are generated. "
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As we can see in Figure 7.3, after about10,000 cycles, its energy is almost.
Completely back to the original mode, no change. Only a few percent of the total energy is reserved for some other vibrations.
Son. (This is not a Poincare cycle, it needs a longer duration. ) this kind
The development of collective mode is a common phenomenon, which can be approximately expressed by the soliton solution of Todag point 3).
Show. The important general feature of soliton solution is that even if the nonlinear coupling is weak, soliton solution
Still exists:
Weak coupling ≠ weak amplitude
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Research on nonlinear problems
E. Fermi, J. basta and S. ulam Literature LA-1900 (May 1955)
abstract
One-dimensional particles composed of 64 particles were studied on the MANIACI computer in Los Alamos.
Dynamic system. There is a nonlinear force between adjacent particles. The nonlinear term considered is quadratic,
Cubic and polyline types. The result is decomposed into Fourier components and plotted as a function of time.
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Since then, there have been a lot of articles about solitons. Scott, Qiu and maclaurin (1973)
A total of ***267 references are listed in the review article of. But all these articles are just about
Classical soliton solutions are almost confined to one-dimensional space at the same time, and only apply to seven special soliton solutions.
As far as equations are concerned: Kotvich-Devry equation, Senna-Gordon equation, etc. Recently in this collar
Great progress has been made in this field, including classical solutions and quantum soliton solutions extended to three-dimensional space.
Some general techniques have been developed, at least in the case of weakly coupled boson fields.
For every classical solution, there is a corresponding quantum solution. These new developments will be ours.
The main part of the discussion.
1) D. J. Korteweg and G. de Vries, Phil. Margo. 39, 422( 1895)
2) Collected Works of Enrico Fermi, edited by E. segre.
(University of Chicago Press, 1965), Volume II, 978 pages.
3) M. Toda，Progr。 Theor。 Physical Supplement 45, 174( 1970).
4) A. C. Scott, F. Y. F. Chu and D. W. Mclaughlin, IEEE 6 1,
144( 1973).
-Introduction to particle physics and field theory Chapter VII Soliton
Li Zhengdao refused to translate Ruan Tongze's Tang Dynasty.
Science Press 1984
Standing on the threshold of the turn of the century, no one can ignore the earth-shaking changes brought by science and technology to mankind in this century. With the birth of computers, the mushroom cloud of atomic bombs enveloped the world, artificial earth satellites and space shuttles traveled in space, and biological cloning technology set off waves all over the world. One hundred years is only a flick of a finger in the long river of human history, but during this period, the development of science and technology far exceeded the sum of the past two thousand years, and the changes to human beings have reached an unprecedented level. As the famous American writer R.W. Emerson said, "The miracles created by modern science far exceed those in ancient myths and legends." The remarkable rise and rapid development of nonlinear science in this century has liberated mankind from cognition, broken a skylight of mechanical determinism, and enabled people to explore a more complex, universal and higher-level world outside the window. In the field of nonlinear science, there is a beautiful "flower of mathematical physics", which, together with the familiar chaos and fractal, is considered as the three frontier branches of this field today, and this is soliton. Soliton, like chaos and fractal, is full of anecdotes and even legends from its discovery to the formation, development and application of theory, and it seems to be more tortuous, which can give us more thinking and enlightenment.
Standing on the threshold of the turn of the century, no one can ignore the earth-shaking changes brought by science and technology to mankind in this century. With the birth of computers, the mushroom cloud of atomic bombs enveloped the world, artificial earth satellites and space shuttles traveled in space, and biological cloning technology set off waves all over the world. One hundred years is only a flick of a finger in the long river of human history, but during this period, the development of science and technology far exceeded the sum of the past two thousand years, and the changes to human beings have reached an unprecedented level. As the famous American writer R.W. Emerson said, "The miracles created by modern science far exceed those in ancient myths and legends." 1 the remarkable rise and rapid development of nonlinear science in this century has liberated mankind from cognition, broken a skylight of mechanical determinism, and enabled people to explore a more complex, more universal and higher-level "outside the window" world. In the field of nonlinear science, there is a beautiful "flower of mathematical physics", which, together with the familiar chaos and fractal, is considered as the three frontier branches of this field today, and this is soliton. Soliton, like chaos and fractal, is full of anecdotes and even legends from its discovery to the formation, development and application of theory, and it seems to be more tortuous, which can give us more thinking and enlightenment.
Monuments by the canal, lonely lonely waves
When it comes to solitons, we have to introduce the discovery process of solitary waves (solitary waves are the earliest concrete forms with soliton properties), and we have to mention a person who belongs to the last century, that is, the discoverer of solitary waves, British scientist and shipbuilding engineer john scott russell. Although the soliton theory was established in the 1950s and 1960s, the discovery of solitary waves can be traced back to the phenomena [2], [3], [4] and [5] that Russell accidentally observed more than 60 years ago.
1834 One day in August, on the bank of the Union Canal in Edinburgh, Scotland, Russell was riding a horse and observing the movement of a ship. The boat was pulled by two horses and sped along the narrow river. When the ship stopped suddenly, Russell saw a wonderful and incredible phenomenon: the water mass pushed in the river did not stop moving, but gathered around the bow and moved violently, and then became a "round, smooth, chiseled, huge and isolated water peak". Suddenly, the water peak left the bow, rolled forward at a fast speed, and continued to sail along the river, with no tendency to slow down and stop. Russell keenly felt that this was an unusual water wave and immediately followed the horse. At this time, the water peak still rolls forward at the speed of 8-9 miles per hour, while maintaining its original shape, about 3 feet long and 1 ~ 1.5 feet high. It was not until he caught up with 1 ~ 2 that the height of the water peak gradually decreased and finally disappeared into the winding river. Russell was attracted by this "strange" and "beautiful" phenomenon. He noticed that this isolated water peak is completely different from ordinary water waves, because in general, water waves always consist of a series of periodic wave trains, which can be described mathematically by a well-known wave equation, and its solution is periodic wave trains. Moreover, the usual water wave is partly above the water surface and partly below the water surface. This water peak is a complete wave all above the water surface. Russell thought that this water peak was a stable solution of fluid mechanics, and named it "translational wave", which was later called "solitary wave". Solitary waves are different from ordinary surface waves because the latter are dispersive; It is also different from the singular shock wave before Apollo, because the waveform of solitary wave is round and smooth, that is, it is regular everywhere.
This accidental discovery haunted Russell's mind for a long time, and he firmly believed that he had discovered a new physical phenomenon. 10 years later, 1844 in September, he reported his findings to scientists at the 14 meeting of the British Association for the Advancement of Science, with the topic of "On Wave", in order to get the attention of the scientific community and study together. During this decade, Russell made a lot of efforts and explorations on the principle of solitary waves and made some bold assumptions in physics. Moreover, he also made an experimental study on solitary waves, and in 1844, he excited them in a shallow water tank in various ways, and observed the same solitary wave phenomenon.
However, history often leaves people with regrets. Russell's idea was not recognized by the scientific authority at that time. Most people doubt and oppose the existence of solitary waves, and once set off a wide and fierce debate. For example, some physicists believe that the decrease of solitary wave amplitude denies its characteristic of keeping its shape and energy unchanged. Russell's explanation is due to friction and resistance. Even so, he still could not correctly explain and prove the existence and mechanism of solitary waves in mathematics and physics, thus complaining that mathematicians at that time could not predict this phenomenon from the known equations of fluid mechanics. "After seeing Wu Gou, I photographed the railing all over, and no one took care of it." I sighed and looked around blankly. Russell finally failed to give Solitary Wave a scientific legal status. 1982, on the centenary of Russell's death, people erected a monument [5] beside the United Canal where he rode in pursuit of solitary waves to commemorate the discoverer of solitary waves, which may have been unexpected before his death. If the mark of a great scientist is that he can identify important new things and phenomena, and these new things and phenomena are indeed key properties, then Russell is worthy of the name [6]. Today, almost all the monographs on soliton theory in various fields first mention this pioneer of soliton theory with reverence. The philosopher Voltaire once said, "The lucky ones who took the lead along the new road won lofty honors in their names, although they only took a few steps." 〔 1〕
After Russell's death, 1895, Dutch mathematician D. Korteweg and his student G. de Vries studied the motion of shallow water waves. Under the assumption of long wave approximation and small amplitude, the motion equation of shallow water wave with one-way motion is established. By solving the analytical solution, the solitary wave solution consistent with Russell's description is obtained, and the existence of solitary wave is proved theoretically for the first time. This equation is the famous KdV equation, and it is also one of the most common models to study soliton solutions. But is solitary wave stable? Are the two solitary waves deformed after collision? These problems have not been solved, and many scientists hold a negative attitude towards it, thinking that solitary waves are "unstable" and giving up further research. Solitary wave once again lost people's attention, was buried for a long time, and continued to spend the first half of the 20th century in solitude.
Big waves wash sand. No one in the world knows you.
"Sometimes the truth may be dim, but it will never go out." 1] The long-term burial and silence of solitary waves does not mean that it has lost its power.
In 1950s, a computer numerical experiment began to change the fate of solitary waves. Starting from 1952, three American physicists, Enrico Fermi, John pasta and Stan ulam, used the Maniac I computer which was used to design hydrogen bombs in the United States at that time, carried out numerical calculation experiments on a system composed of 64 harmonic oscillators with weak nonlinear interaction with each other, trying to confirm the "energy equipartition theorem" in statistical physics. At the initial moment, the energy of these oscillators is all concentrated on one oscillator, and the initial energy of the other 63 oscillators is zero. According to the theorem of energy equipartition, as long as the nonlinear effect exists, there will be phenomena such as energy equipartition and ergodicity, that is, any weak nonlinear interaction can lead to the transition from non-equilibrium state to equilibrium state. However, the calculation result of 1955 surprised them, because after tens of thousands of calculations for a long time, the energy was not evenly distributed to other oscillators, but there was a strange "backflow" phenomenon: most of the energy was concentrated on the original harmonic oscillator with non-zero initial energy. The classical energy equipartition theorem has not been proved. This is the famous FPU problem, which, like the Michelson-Morey experiment that gave birth to Einstein's theory of relativity, is considered as a powerful challenge to traditional science [2] and [6].
Unfortunately, at that time, Fermi and others only investigated the experiment in frequency space, and did not find the solitary wave solution and got the correct explanation, so they missed the soliton theory. Later, people regarded the crystal as a mass chain connected by a spring, which approximately simulated this situation. Toda studied the nonlinear vibration of this mode, and indeed got the solitary wave solution, which made the FPU problem solved correctly.
The appearance and solution of FPU problem depends on the newly born computer technology, which proves the existence of solitary waves to people by numerical calculation for the first time, thus further arousing people's interest in the study of solitary waves. In 1962, Perring and Skyrme applied the sine-Godan equation to the study of elementary particles. Their calculation results show that such solitary waves are not dispersed, and even after two solitary waves collide, they still maintain their original shape and speed. 1965, two mathematicians of Princeton University, M. D. Kruskal and N. Zabusky, based on the FPU problem, linked the almost regression property of energy distribution in the experiment with the peculiar interaction property of solitary waves, and studied the nonlinear interaction process of solitary wave collision in plasma in detail by numerical simulation. A relatively complete and rich result is obtained, which further proves that the waveform and velocity of solitary waves remain unchanged after collision, and this result completely dispels people's previous doubts about the stability of solitary waves.
Kruskal and Zabusky were officially named "solitons" according to the fact that the properties of solitary waves and particles are similar after collision. This is an important milestone for Solitary Wave to walk out of the cold palace of science. From the discovery of solitary wave to the formal proposal of the concept of soliton, it has gone through a long journey of 130 years, in which the ups and downs are rare in the history of modern science. At this point, the soliton, known as the "flower of mathematical physics", has finally washed away the dust for more than a century, stood the test of time and displayed its beautiful buds in the scientific garden.
The concept of soliton opens a new era of soliton theory research, and scientists in various fields have devoted great enthusiasm and interest to soliton. At this point, the soliton theory of a relatively complete system has gradually formed. Today mathematicians understand the definition of soliton as the local traveling wave solution of nonlinear evolution equation. After colliding with each other, the waveform and velocity will not change, but the phase may change. Physicists understand the nonlinear evolution equation as a solution with limited energy, that is, energy is concentrated in a limited area of space and does not spread to an infinite area with the increase of time [5].
The initial research of soliton theory mainly focused on mathematical problems. In 1967, Gardner et al. discovered the inverse scattering method (IST) for solving the KdV equation. Subsequently, people discovered at least dozens of nonlinear equations with soliton solutions except KdV equation, and developed colorful and effective mathematical and physical methods [3], [5] and [7]. With the deepening of research, scientists are not satisfied with studying solitons in the form of pure mathematics, and try to find other types of solitons in areas other than fluid mechanics. The result is very exciting, and people have found solitons in different natural science fields. For example, scientists have found that there are various types of solitons in the protein and DNA of biological macromolecules, and these solitons shoulder an indispensable responsibility in life activities: transmitting biological energy and biological information, and completing the functions of replication, inheritance and transcription [8]. So far, it can be said that soliton phenomenon is everywhere: density wave, ocean shock wave, plasma, molecular system, biological system, optical transmission in optical fiber, laser propagation, superconducting Josephson junction, magnetism, structural phase transition, liquid crystal and so on. , you can find the magic figure of soliton [4]. The "Flower of Mathematical Physics" soliton shows wonderful charm in the microscopic world of the universe and elementary particles, attracting more and more scientists.
A scientist once said, "The whole history of scientific development proves that any new field of mastering natural phenomena will always move towards practical application. This practical application is often completely unexpected. " So is the discovery of [1] soliton. Although soliton seems to be only the solution of a mathematical nonlinear equation or a phenomenon found in the laboratory, people soon found its application in practice. The most typical example is the application of optical soliton in modern communication technology [4], [9]. 1973, scientists proposed and predicted the existence of optical solitons. 1980 was confirmed in the experiment. Optical soliton is the best information carrier based on photoelectric communication means because of its advantages of no waveform loss, constant speed, high fidelity and good confidentiality, and is favored by scientists. People naturally hope to apply it to modern optical fiber communication, thus producing modern optical fiber soliton communication technology. This high-tech is constantly developing and has begun to enter some practical stages. By the mid-1990s, optical solitons had been transmitted to 1000km and 1 000,000 km without deformation (the latter needs regeneration). Scientists earnestly hope that in the future communication technology, optical soliton can exert its great power, so that everyone on the earth can enjoy the speed and convenience brought by optical fiber soliton communication.
Thinking and Enlightenment —— Not "Debate on Xuanzong's Grand Ceremony"
After the concept of soliton was put forward, this field attracted thousands of scientists, including researchers engaged in more and more fields such as mathematics, mechanics, physics, biology and optics, which made the soliton theory develop rapidly in the past thirty years. It can be said that soliton research is in the ascendant, and continues to go deep into a more complex, broader and more essential level. When we open the history of modern science and look back at soliton, the "flower of mathematical physics" 100 years of historical fate from today's perspective, we should be able to deeply understand that it is also a microcosm of the century-old history of modern science and technology. "Many things are ridiculous in ancient and modern times." From Russell's discovery of solitary waves to the display of optical solitons, from the KdV equation to the vast mathematical theory works of solitons, all of them are stories that can always be talked about. However, for scientists and scientists, in addition to "sitting still" or "laughing", perhaps more important is the thinking that this history has brought us. Here we have to ask: Why didn't Russell's discovery more than 60 years ago lead to the emergence of soliton theory at that time? In other words, why did soliton theory enter the scientific stage after 1950s?
In fact, there are many examples in the history of science and technology, such as the historical fate of solitons. According to historical records [1 1], human beings have long known the principle of steam. As early as 120 BC, the ancient Greeks made machinery driven by steam according to the principle of jet reaction. But they didn't use it to promote production tools or warships, because there was no such demand at that time. It was just a strange skill and enjoyed in palaces and temples. It was not until17th century that steam technology was valued, improved and innovated due to the needs of mining and metallurgy industry, which triggered an unprecedented technological revolution and industrial revolution in history, and thus developed a new discipline-thermodynamics. Looking at the development of science and technology in the 20th century, it has not been divorced from the laws of history. The historical fate of Orphan vividly and profoundly illustrates this point.
Russell discovered and explored solitary waves at the end of the British industrial revolution, the beginning of the chemical technology revolution and the electric power technology revolution in history, and the great era when machine production replaced manual production. This era is characterized by the unprecedented development of the western economy, which calls for the scientific theory and technological revolution it needs and makes it full of forward vitality. The building of classic natural science has been basically built on the wisdom of stars such as Newton, and science is in the era of mechanical determinism. Newton's achievements in classical mathematics, mechanics and optics, the "interpreter of the universe", represent the highest peak of mechanical determinism and have dominated people's scientific thinking since then. Laplace elaborated this brilliantly. He believes that the image of a complex world, like the structure and order of mechanical parts, cannot escape the insight of the so-called "super-intelligent". For "super smart people", "he can probably infer the motion from the largest object to the lightest atom in the universe with a mathematical formula." "Probably nothing is uncertain. The future, like the past, will be presented to him. " One consequence of mechanical determinism is that people are obsessed with the mathematical and physical methods of deterministic and linear problems, and perfected and mastered them at that time. Although this scientific thought was broken through after the 20th century, it made great achievements in its era: on the one hand, it promoted the rapid development of various branches of classical natural science, laid a theoretical foundation for technological revolution, on the other hand, it greatly promoted the progress of social production. The development of industrial production and the technical level at that time could not put forward the "extraordinary" requirements for classical natural science beyond that era. Therefore, although there have been interesting nonlinear problems in Newtonian mechanics (such as fixed-point motion of rigid body and three-body motion), scientists are far from being "forced" to study nonlinear problems. We know that soliton is essentially a nonlinear result. In Russell's time, industrial production, technological change and the development of scientific theory could not put forward urgent demand for soliton research. This is the fundamental reason why solitary waves did not attract people's attention in the last century. Although Russell discovered solitary waves with his keen insight and profound grasp of the physical essence of things, he could not surpass the domination of mechanical determinism on the scientific thought of that era. At first, he could not get the answer to the question in mathematics. Similarly, more than 60 years later, the result of KdV equation is only a mathematical "coincidence", which can not change the fate of solitary wave being buried. Therefore, assuming that the discovery of solitary waves is delayed for decades or even a century (just like the discovery of chaos after the 1960s), the emergence and development of soliton theory will probably not be greatly affected. In this sense, Russell, like a lonely pioneer, accidentally broke into the door of a new treasure house, but he didn't and couldn't get the spell of "open sesame". Of course, this can't deny his contribution to the later soliton theory, let alone demand him for it, just as we can't demand the ancient Greeks to make steam engines.
After entering the 20th century, a physical revolution marked by the birth of relativity and quantum mechanics broke out in the field of natural science, and people's exploration and understanding of the world reached an unprecedented depth from both macro and micro perspectives. The evolution of celestial bodies, the change of the earth and the origin of life all involve the evolution law of extremely complex systems. It is urgent for people to study the basic laws of these complex phenomena and explore and grasp nature from the perspective of the overall connection closer to the essence of the world. [10] Only when people devote themselves to the study of nonlinear problems can solitons get out of the cold palace of science.
In the 20th century after World War II, mankind ushered in a new era of super-high-speed development of science and technology. The competition of comprehensive national strength in economy, armament and technology among countries in the world has fundamentally promoted the ultra-high-speed development of modern science and technology. According to statistics [10], the investment of scientific research funds in all developed countries increased exponentially after the war, and the global scientific research funds increased by 400 times by the end of 1960s compared with the beginning of this century. The development of human society has never been so dependent on science and technology as this century. At the beginning of this century, only 5% ~ 20% of the production growth in developed countries depended on science and technology, but it has reached 60% ~ 70% in the 1970s. It is in this "great demand" that science and technology are developing rapidly. Scientists' tentacles are constantly deepening and extending, new knowledge and laws are constantly being discovered, and various new disciplines and fields are constantly emerging. Taking soliton as an example, the FPU problem is not to study soliton at first, but to investigate the motion law of complex dynamic system simulating anharmonic lattice, and finally the soliton phenomenon is discovered unexpectedly. It is worth noting that military demand plays an inestimable role in the development of modern science and technology. As we all know, ENIAC, the first electronic computer, was made to solve the complex ballistic calculation problem. The tool for finding soliton-like FPU problem by numerical calculation is Maniac I, a large computer used by the United States to design hydrogen bombs. It is not difficult to imagine that if it is not for military purposes, the computer age of mankind may be postponed, and the wide application of computer technology in non-military fields and many major scientific and technological discoveries will be rewritten. Therefore, after the war in this century, various social factors have a strong demand for the development of science and technology, and science and technology itself has deepened and complicated.