"Solitons"의 두 판 사이의 차이

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<h5>introduction</h5>
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==introduction==
  
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* Solitons were discovered experimentally (Russell 1844)
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*  analytically (Korteweg & de Vries, 1895)
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** modelling of Russell's discovery
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** 1-soliton solution
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*  numerically (Zabusky & Kruskal 1965).
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** interaction of two 1-soliton solutions
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** they discovered that solitons of differenct sizes interact cleanly
  
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<h5>history</h5>
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==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)
 +
 
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==PDEs==
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* [[KdV equation]]
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* [[sine-Gordon equation]]
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* [[Nonlinear Schrodinger equation|Non-linear Schrodinger equation]]
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==important techniques==
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* [[Lax pair formulation]]
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* [[inverse scattering method]]
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==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
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*  
 
  
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==하위페이지==
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* [[solitons]]
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* [[Boussinesq equation]]
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* [[course design on soliton]]
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* [[Fermi-Pasta-Ulam problem]]
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* [[Frenkel-Kontorova dislocation]]
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* [[Hamiltonian structure in soliton theory|Hamiltonian structure]]
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* [[Kadometsev-Petviashvii equation (KP equation)]]
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* [[KdV equation]]
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* [[0 methods and theory|methods and theory]]
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* [[algebro-geometric method in soliton theory]]
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* [[Bäcklund transformation (backlund)]]
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* [[Tau functions and Bethe ansatz|Bethe ansatz and Tau functions]]
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* [[hierarchy of soliton equations]]
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* [[Hirota bilinear method]]
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* [[inverse scattering method]]
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* [[quantization of solitons and quantum inverse scattering method (QISM)]]
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* [[Sato theory]]
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* [[tau functions]]
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* [[Nonlinear Schrodinger equation]]
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* [[quantum sine-Gordon field theory]]
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* [[restricted sine-Gordon theory]]
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* [[sine-Gordon equation]]
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* [[Topological solitons]]
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==related items==
  
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* [[inverse scattering method]]
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* [[5720447|wave phenomema]]
  
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<h5>related items</h5>
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==computational resource==
  
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<h5>books</h5>
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* [[KdV equation]]
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* [[sine-Gordon equation]][[5398019/attachments/3290825|5398019/attachments/3290825]]
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* [http://physics.ucsc.edu/%7Epeter/250/mathematica/ ][http://physics.ucsc.edu/%7Epeter/250/mathematica/ http://physics.ucsc.edu/~peter/250/mathematica/]
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** [[5398019/attachments/3290823|soliton.nb]]
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** [[5398019/attachments/3290825|sinegordon.nb]]
  
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* [[2009년 books and articles|찾아볼 수학책]]
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
  
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==books==
  
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<h5>encyclopedia</h5>
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* [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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* Soliton, Toda
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* Theory of Nonlinear Lattices, Morikazu Toda
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* Nonlinear evolution equations solvable by the spectral transform, Eds. Calogero, 1977
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* Solitons and Nonlinear Wave Equations, R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, H.C.Morries, Academic Press, London, 1982
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* [[2010년 books and articles]]
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==encyclopedia==
  
 
* 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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* http://en.wikipedia.org/wiki/
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* http://en.wikipedia.org/wiki/
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* http://en.wikipedia.org/wiki/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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==expositions==
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* Sascha Vongehr [http://physics1.usc.edu/~vongehr/solitons_html/solitons.html Solitons in field theory], 1997
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* [http://arxiv.org/abs/0802.2408 Why are solitons stable?] Terence Tao, 2008[http://xxx.lanl.gov/abs/q-alg/9712005 ]
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* [http://www.ma.utexas.edu/users/uhlen/solitons/notes.pdf An Introduction to Wave Equations and Solitons] Richard S. Palais
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* 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
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* 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==
  
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<h5>blogs</h5>
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* [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
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* [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
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* [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
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* 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.
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* 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.
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* [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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* 구글 블로그 검색<br>
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** http://blogsearch.google.com/blogsearch?q=
 
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** http://blogsearch.google.com/blogsearch?q=
 
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** http://blogsearch.google.com/blogsearch?q=
 
  
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<h5>articles</h5>
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==question and answers(Math Overflow)==
  
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* [http://xxx.lanl.gov/abs/q-alg/9712005 Five Lectures on Soliton Equations]<br>
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* http://mathoverflow.net/search?q=
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** Edward Frenkel, Submitted on 30 Nov 1997
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* http://mathoverflow.net/search?q=
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* [[2010년 books and articles|논문정리]]
 
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* http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
 
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* http://www.zentralblatt-math.org/zmath/en/
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 
  
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* http://www.ams.org/mathscinet
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
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* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
 
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* http://dx.doi.org/
 
  
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[[분류:개인노트]]
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[[분류:integrable systems]]
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[[분류:math and physics]]
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[[분류:migrate]]
  
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<h5>TeX </h5>
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q464949 Q464949]
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===Spacy 패턴 목록===
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* [{'LEMMA': 'soliton'}]
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* [{'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


related items



computational resource



books


encyclopedia



expositions



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

Spacy 패턴 목록

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