Solitons

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

• KdV equation
• sine-Gordon equation
• Non-linear Schrodinger equation

important techniques

• Lax pair formulation
• inverse scattering method

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=soliton

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

related items

• inverse scattering method
• wave phenomema

computational resource

• KdV equation
• sine-Gordon equation5398019/attachments/3290825
• [1]http://physics.ucsc.edu/~peter/250/mathematica/
  • soliton.nb
  • sinegordon.nb

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

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Soliton

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)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

메타데이터

위키데이터

• ID : Q464949

Spacy 패턴 목록

• [{'LEMMA': 'soliton'}]
• [{'LOWER': 'soliton'}, {'LEMMA': 'wave'}]