"Solitons"의 두 판 사이의 차이
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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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2014년 4월 13일 (일) 20:43 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
- 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)