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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* Solitons were discovered experimentally (Russell 1844) | * Solitons were discovered experimentally (Russell 1844) | ||
| 13번째 줄: | 13번째 줄: | ||
| − | ==meaning of soliton | + | ==meaning of soliton== |
* "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons | * "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons | ||
| 22번째 줄: | 22번째 줄: | ||
| − | ==PDEs | + | ==PDEs== |
* [[KdV equation]] | * [[KdV equation]] | ||
| 32번째 줄: | 32번째 줄: | ||
| − | ==important techniques | + | ==important techniques== |
* [[Lax pair formulation]] | * [[Lax pair formulation]] | ||
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| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q=soliton | * http://www.google.com/search?hl=en&tbs=tl:1&q=soliton | ||
| 80번째 줄: | 80번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[inverse scattering method]] | * [[inverse scattering method]] | ||
| 89번째 줄: | 89번째 줄: | ||
| − | ==computational resource | + | ==computational resource== |
* [[KdV equation]] | * [[KdV equation]] | ||
| 101번째 줄: | 101번째 줄: | ||
| − | ==books | + | ==books== |
* [http://gigapedia.com/items/428472/integrable-models--world-scientific-lecture-notes-in-physics- Integrable Models (World Scientific Lecture Notes in Physics)]Ashok Das | * [http://gigapedia.com/items/428472/integrable-models--world-scientific-lecture-notes-in-physics- Integrable Models (World Scientific Lecture Notes in Physics)]Ashok Das | ||
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| − | ==encyclopedia | + | ==encyclopedia== |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 134번째 줄: | 134번째 줄: | ||
| − | ==expositions | + | ==expositions== |
* [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 ] | ||
| 145번째 줄: | 145번째 줄: | ||
| − | ==articles | + | ==articles== |
* [http://dx.doi.org/10.1098/rspa.1999.0502%20 Solitons, Links and Knots]Richard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331 | * [http://dx.doi.org/10.1098/rspa.1999.0502%20 Solitons, Links and Knots]Richard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331 | ||
| 164번째 줄: | 164번째 줄: | ||
| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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| − | ==blogs | + | ==blogs== |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 183번째 줄: | 183번째 줄: | ||
| − | ==experts on the field | + | ==experts on the field== |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | ==links | + | ==links== |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 14:42 판
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
- Nonlinear Schrodinger equation
- quantum sine-Gordon field theory
- restricted sine-Gordon theory
- sine-Gordon equation
- Boussinesq equation
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
- http://gigapedia.info/1/soliton
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Soliton
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
expositions
- 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.
question and answers(Math Overflow)
blogs
experts on the field