"Solitons"의 두 판 사이의 차이
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| 6번째 줄: | 6번째 줄: | ||
* numerically (Zabusky & Kruskal 1965).<br> | * numerically (Zabusky & Kruskal 1965).<br> | ||
** they discovered that solitons of differenct sizes interact cleanly | ** they discovered that solitons of differenct sizes interact cleanly | ||
| + | ** interaction of two 1-soliton solutions | ||
| 13번째 줄: | 14번째 줄: | ||
<h5>meaning of soliton</h5> | <h5>meaning of soliton</h5> | ||
| − | * | + | * "soliton" is used to describe their particle-like properties like bosons, fermions and hadrons |
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* 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) | * 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) | ||
| 66번째 줄: | 64번째 줄: | ||
* [[solitons|soliton]]<br> | * [[solitons|soliton]]<br> | ||
** [[Bäcklund transformation (backlund)|Bäcklund transformation]]<br> | ** [[Bäcklund transformation (backlund)|Bäcklund transformation]]<br> | ||
| + | ** [[Frenkel-Kontorova dislocation]]<br> | ||
** [[Hirota bilinear method|Hirota hierarchy]]<br> | ** [[Hirota bilinear method|Hirota hierarchy]]<br> | ||
** [[inverse scattering method]]<br> | ** [[inverse scattering method]]<br> | ||
| 72번째 줄: | 71번째 줄: | ||
** [[Nonlinear Schrodinger equation]]<br> | ** [[Nonlinear Schrodinger equation]]<br> | ||
** [[quantum sine-Gordon field theory]]<br> | ** [[quantum sine-Gordon field theory]]<br> | ||
| + | ** [[restricted sine-Gordon theory]]<br> | ||
** [[sine-Gordon equation]]<br> | ** [[sine-Gordon equation]]<br> | ||
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| 128번째 줄: | 127번째 줄: | ||
<h5>expositions</h5> | <h5>expositions</h5> | ||
| + | * [http://arxiv.org/abs/0802.2408 Why are solitons stable?]<br> | ||
| + | ** Terence Tao, 2008 | ||
| + | * [http://xxx.lanl.gov/abs/q-alg/9712005 Five Lectures on Soliton Equations]<br> | ||
| + | ** Edward Frenkel, Submitted on 30 Nov 1997 | ||
* 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 | * 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/10.1216/RMJ-1978-8-1-413 A brief history of the quantum soliton with new results on the quantization of the Toda lattice]<br> | * [http://dx.doi.org/10.1216/RMJ-1978-8-1-413 A brief history of the quantum soliton with new results on the quantization of the Toda lattice]<br> | ||
| 138번째 줄: | 141번째 줄: | ||
<h5>articles</h5> | <h5>articles</h5> | ||
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* [http://dx.doi.org/10.1098/rspa.1999.0502%20 Solitons, Links and Knots]<br> | * [http://dx.doi.org/10.1098/rspa.1999.0502%20 Solitons, Links and Knots]<br> | ||
** Richard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331 | ** 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]<br> | * [http://www.ams.org/journals/bull/1997-34-04/S0273-0979-97-00732-5/home.html The Symmetries of Solitons]<br> | ||
** Richard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403 | ** Richard S. Palais, Journal: Bull. Amer. Math. Soc. 34 (1997), 339-403 | ||
2011년 1월 25일 (화) 04:40 판
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
- interaction of two 1-soliton solutions
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
mathematica code
history
하위페이지
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
- Five Lectures on Soliton Equations
- Edward Frenkel, Submitted on 30 Nov 1997
- 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
- 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
- Solitons, Links and Knots
- Richard Battye, Paul Sutcliffe, Proc. R. Soc. Lond. A 8 December 1999 vol. 455 no. 1992 4305-4331
- 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.
question and answers(Math Overflow)
blogs
experts on the field