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| 2번째 줄: | 2번째 줄: | ||
* Solitons were discovered experimentally (Russell 1844) | * Solitons were discovered experimentally (Russell 1844) | ||
| − | * analytically (Korteweg & de Vries, 1895) | + | * analytically (Korteweg & de Vries, 1895) |
** modelling of Russell's discovery | ** modelling of Russell's discovery | ||
** 1-soliton solution | ** 1-soliton solution | ||
| − | * numerically (Zabusky & Kruskal 1965). | + | * numerically (Zabusky & Kruskal 1965). |
** interaction of two 1-soliton solutions | ** interaction of two 1-soliton solutions | ||
** they discovered that solitons of differenct sizes interact cleanly | ** they discovered that solitons of differenct sizes interact cleanly | ||
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==meaning of soliton== | ==meaning of soliton== | ||
| − | * "soliton" is used to describe their particle-like properties like bosons, fermions | + | * "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons |
* any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift) | * any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift) | ||
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==PDEs== | ==PDEs== | ||
| 28번째 줄: | 28번째 줄: | ||
* [[Nonlinear Schrodinger equation|Non-linear Schrodinger equation]] | * [[Nonlinear Schrodinger equation|Non-linear Schrodinger equation]] | ||
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==important techniques== | ==important techniques== | ||
| 37번째 줄: | 37번째 줄: | ||
* [[inverse scattering method]] | * [[inverse scattering method]] | ||
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==history== | ==history== | ||
| 45번째 줄: | 45번째 줄: | ||
* http://www.google.com/search?hl=en&tbs=tl:1&q=soliton | * http://www.google.com/search?hl=en&tbs=tl:1&q=soliton | ||
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| − | + | ==하위페이지== | |
| − | + | * [[solitons]] | |
| − | * [[solitons]] | + | * [[Boussinesq equation]] |
| − | + | * [[course design on soliton]] | |
| − | + | * [[Fermi-Pasta-Ulam problem]] | |
| − | + | * [[Frenkel-Kontorova dislocation]] | |
| − | + | * [[Hamiltonian structure in soliton theory|Hamiltonian structure]] | |
| − | + | * [[Kadometsev-Petviashvii equation (KP equation)]] | |
| − | + | * [[KdV equation]] | |
| − | + | * [[0 methods and theory|methods and theory]] | |
| − | + | * [[algebro-geometric method in soliton theory]] | |
| − | + | * [[Bäcklund transformation (backlund)]] | |
| − | + | * [[Tau functions and Bethe ansatz|Bethe ansatz and Tau functions]] | |
| − | + | * [[hierarchy of soliton equations]] | |
| − | + | * [[Hirota bilinear method]] | |
| − | + | * [[inverse scattering method]] | |
| − | + | * [[quantization of solitons and quantum inverse scattering method (QISM)]] | |
| − | + | * [[Sato theory]] | |
| − | + | * [[tau functions]] | |
| − | + | * [[Nonlinear Schrodinger equation]] | |
| − | + | * [[quantum sine-Gordon field theory]] | |
| − | + | * [[restricted sine-Gordon theory]] | |
| − | + | * [[sine-Gordon equation]] | |
| − | + | * [[Topological solitons]] | |
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==related items== | ==related items== | ||
| 85번째 줄: | 83번째 줄: | ||
* [[5720447|wave phenomema]] | * [[5720447|wave phenomema]] | ||
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==computational resource== | ==computational resource== | ||
| 93번째 줄: | 91번째 줄: | ||
* [[KdV equation]] | * [[KdV equation]] | ||
* [[sine-Gordon equation]][[5398019/attachments/3290825|5398019/attachments/3290825]] | * [[sine-Gordon equation]][[5398019/attachments/3290825|5398019/attachments/3290825]] | ||
| − | * [http://physics.ucsc.edu/%7Epeter/250/mathematica/ ][http://physics.ucsc.edu/%7Epeter/250/mathematica/ http://physics.ucsc.edu/~peter/250/mathematica/] | + | * [http://physics.ucsc.edu/%7Epeter/250/mathematica/ ][http://physics.ucsc.edu/%7Epeter/250/mathematica/ http://physics.ucsc.edu/~peter/250/mathematica/] |
** [[5398019/attachments/3290823|soliton.nb]] | ** [[5398019/attachments/3290823|soliton.nb]] | ||
** [[5398019/attachments/3290825|sinegordon.nb]] | ** [[5398019/attachments/3290825|sinegordon.nb]] | ||
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==books== | ==books== | ||
| 106번째 줄: | 104번째 줄: | ||
* Soliton, Toda | * Soliton, Toda | ||
* Theory of Nonlinear Lattices, Morikazu Toda | * Theory of Nonlinear Lattices, Morikazu Toda | ||
| − | * Nonlinear evolution equations solvable by the spectral transform, Eds. Calogero, | + | * Nonlinear evolution equations solvable by the spectral transform, Eds. Calogero, 1977 |
| − | * Solitons and Nonlinear Wave Equations, R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, H.C.Morries, | + | * Solitons and Nonlinear Wave Equations, R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, H.C.Morries, Academic Press, London, 1982 |
* [[2010년 books and articles]] | * [[2010년 books and articles]] | ||
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==encyclopedia== | ==encyclopedia== | ||
| 116번째 줄: | 114번째 줄: | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/Soliton | * http://en.wikipedia.org/wiki/Soliton | ||
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==expositions== | ==expositions== | ||
| 124번째 줄: | 122번째 줄: | ||
* [http://arxiv.org/abs/0802.2408 Why are solitons stable?] Terence Tao, 2008[http://xxx.lanl.gov/abs/q-alg/9712005 ] | * [http://arxiv.org/abs/0802.2408 Why are solitons stable?] Terence Tao, 2008[http://xxx.lanl.gov/abs/q-alg/9712005 ] | ||
* [http://www.ma.utexas.edu/users/uhlen/solitons/notes.pdf An Introduction to Wave Equations and Solitons] Richard S. Palais | * [http://www.ma.utexas.edu/users/uhlen/solitons/notes.pdf An Introduction to Wave Equations and Solitons] Richard S. Palais | ||
| − | * Richard S Palais, “The Symmetries of Solitons,” dg-ga/9708004 (August 8, 1997), http://arxiv.org/abs/dg-ga/9708004. | + | * Richard S Palais, “The Symmetries of Solitons,” dg-ga/9708004 (August 8, 1997), http://arxiv.org/abs/dg-ga/9708004. [http://dx.doi.org/10.1090/S0273-0979-97-00732-5 ]http://dx.doi.org/10.1090/S0273-0979-97-00732-5 |
| − | * Ford, Joseph. 1992. The Fermi-Pasta-Ulam problem: Paradox turns discovery. Physics Reports 213, no. 5 (May): 271-310. doi:[http://dx.doi.org/10.1016/0370-1573%2892%2990116-H 10.1016/0370-1573(92)90116-H]. | + | * Ford, Joseph. 1992. The Fermi-Pasta-Ulam problem: Paradox turns discovery. Physics Reports 213, no. 5 (May): 271-310. doi:[http://dx.doi.org/10.1016/0370-1573%2892%2990116-H 10.1016/0370-1573(92)90116-H]. [http://dx.doi.org/10.1216/RMJ-1978-8-1-413 ] |
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==articles== | ==articles== | ||
| 135번째 줄: | 133번째 줄: | ||
* [http://www.ams.org/journals/bull/1997-34-04/S0273-0979-97-00732-5/home.html The Symmetries of Solitons]Richard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403 | * [http://www.ams.org/journals/bull/1997-34-04/S0273-0979-97-00732-5/home.html The Symmetries of Solitons]Richard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403 | ||
* [http://dx.doi.org/10.1143/PTPS.94.1%20 From Solitons to Knots and Links] Miki Wadati and Yasuhiro Akutsu, Prog. Theor. Phys. Supplement No.94 (1988) pp. 1-41 | * [http://dx.doi.org/10.1143/PTPS.94.1%20 From Solitons to Knots and Links] Miki Wadati and Yasuhiro Akutsu, Prog. Theor. Phys. Supplement No.94 (1988) pp. 1-41 | ||
| − | * Lax, P. D. 1996. Outline of a Theory of the KdV | + | * Lax, P. D. 1996. Outline of a Theory of the KdV Equation in Recent Mathematical Methods in Nonlinear Wave Propagation. Lecture Notes in Mathematics, volume 1640, pp. 70–102. New York: Springer. |
* Russell, J. S. 1844. Report on waves. In Report of the 14th Meeting of the British Association for the Advancement of Science, pp. 311–90. London: John Murray. | * Russell, J. S. 1844. Report on waves. In Report of the 14th Meeting of the British Association for the Advancement of Science, pp. 311–90. London: John Murray. | ||
* Toda, M. 1989. Nonlinear Waves and Solitons. Dordrecht: Kluwer. | * Toda, M. 1989. Nonlinear Waves and Solitons. Dordrecht: Kluwer. | ||
| 141번째 줄: | 139번째 줄: | ||
* [http://dx.doi.org/10.1216/RMJ-1978-8-1-413 http://dx.doi.org/10.1090/S0273-0979-97-00732-5] | * [http://dx.doi.org/10.1216/RMJ-1978-8-1-413 http://dx.doi.org/10.1090/S0273-0979-97-00732-5] | ||
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==question and answers(Math Overflow)== | ==question and answers(Math Overflow)== | ||
| 150번째 줄: | 148번째 줄: | ||
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q464949 Q464949] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LEMMA': 'soliton'}] | ||
| + | * [{'LOWER': 'soliton'}, {'LEMMA': 'wave'}] | ||
2021년 2월 17일 (수) 01:39 기준 최신판
introduction
- Solitons were discovered experimentally (Russell 1844)
- analytically (Korteweg & de Vries, 1895)
- modelling of Russell's discovery
- 1-soliton solution
- numerically (Zabusky & Kruskal 1965).
- interaction of two 1-soliton solutions
- they discovered that solitons of differenct sizes interact cleanly
meaning of soliton
- "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons
- any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
PDEs
important techniques
history
하위페이지
- solitons
- Boussinesq equation
- course design on soliton
- Fermi-Pasta-Ulam problem
- Frenkel-Kontorova dislocation
- Hamiltonian structure
- Kadometsev-Petviashvii equation (KP equation)
- KdV equation
- methods and theory
- algebro-geometric method in soliton theory
- Bäcklund transformation (backlund)
- Bethe ansatz and Tau functions
- hierarchy of soliton equations
- Hirota bilinear method
- inverse scattering method
- quantization of solitons and quantum inverse scattering method (QISM)
- Sato theory
- tau functions
- Nonlinear Schrodinger equation
- quantum sine-Gordon field theory
- restricted sine-Gordon theory
- sine-Gordon equation
- Topological solitons
computational resource
- KdV equation
- sine-Gordon equation5398019/attachments/3290825
- [1]http://physics.ucsc.edu/~peter/250/mathematica/
books
- Integrable Models (World Scientific Lecture Notes in Physics)Ashok Das
- Soliton, Toda
- Theory of Nonlinear Lattices, Morikazu Toda
- Nonlinear evolution equations solvable by the spectral transform, Eds. Calogero, 1977
- Solitons and Nonlinear Wave Equations, R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, H.C.Morries, Academic Press, London, 1982
- 2010년 books and articles
encyclopedia
expositions
- Sascha Vongehr Solitons in field theory, 1997
- Why are solitons stable? Terence Tao, 2008[2]
- An Introduction to Wave Equations and Solitons Richard S. Palais
- Richard S Palais, “The Symmetries of Solitons,” dg-ga/9708004 (August 8, 1997), http://arxiv.org/abs/dg-ga/9708004. [3]http://dx.doi.org/10.1090/S0273-0979-97-00732-5
- Ford, Joseph. 1992. The Fermi-Pasta-Ulam problem: Paradox turns discovery. Physics Reports 213, no. 5 (May): 271-310. doi:10.1016/0370-1573(92)90116-H. [4]
articles
- Solitons, Links and KnotsRichard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331
- The Symmetries of SolitonsRichard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403
- From Solitons to Knots and Links Miki Wadati and Yasuhiro Akutsu, Prog. Theor. Phys. Supplement No.94 (1988) pp. 1-41
- Lax, P. D. 1996. Outline of a Theory of the KdV Equation in Recent Mathematical Methods in Nonlinear Wave Propagation. Lecture Notes in Mathematics, volume 1640, pp. 70–102. New York: Springer.
- Russell, J. S. 1844. Report on waves. In Report of the 14th Meeting of the British Association for the Advancement of Science, pp. 311–90. London: John Murray.
- Toda, M. 1989. Nonlinear Waves and Solitons. Dordrecht: Kluwer.
- Zabusky, N. J., and M. D. Kruskal. 1965. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Physics Review Letters 15:240–43.
- http://dx.doi.org/10.1090/S0273-0979-97-00732-5
question and answers(Math Overflow)
메타데이터
위키데이터
- ID : Q464949
Spacy 패턴 목록
- [{'LEMMA': 'soliton'}]
- [{'LOWER': 'soliton'}, {'LEMMA': 'wave'}]