Solitons

introduction

• Solitons were discovered experimentally (Russell 1844)
• analytically (Korteweg & de Vries, 1895)
  
  • modelling of Russell's discovery
• numerically (Zabusky & Kruskal 1965).
  
  • they discovered that solitons of differenct sizes interact cleanly

 

 

meaning of soliton

• "soliton" is used to describe their particle-like properties
  
  • boson
  • fermion
  • hadron

 

 

 

PDEs

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

 

 

important techniques

• Lax pair formulation
• inverse scattering method

 

 

 

toda lattice solitons

• http://www.phys.hawaii.edu/~teb/optics/java/toda/

 

 

mathematica code

• KdV equation
  
  • soliton.nb
• sine-Gordon equation
  
  • sinegordon.nb
• http://physics.ucsc.edu/~peter/250/mathematica/

 

history

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

 

 

 

하위페이지

• soliton
  
  • Bäcklund transformation
    
  • Hirota hierarchy
    
  • inverse scattering method
    
  • KdV equation
    
  • KP hierarchy
    
  • Nonlinear Schrodinger equation
    
  • quantum sine-Gordon field theory
    
  • sine-Gordon equation
    
  • Toda lattice
    

 

 

related items

• inverse scattering method
• wave phenomema

 

 

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)

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

expositions

A brief history of the quantum soliton with new results on the quantization of the Toda lattice
Bill Sutherland, Rocky Mountain J. Math. Volume 8, Number 1-2 (1978), 413-430.

 

 

articles

• Why are solitons stable?
  
  • Terence Tao, 2008
• Solitons, Links and Knots
  
  • Richard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331
• Five Lectures on Soliton Equations
  
  • Edward Frenkel, Submitted on 30 Nov 1997
• The Symmetries of Solitons
  
  • Richard 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.

• 논문정리
• http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html

• http://www.ams.org/mathscinet
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• 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=
• http://dx.doi.org/10.1216/RMJ-1978-8-1-413