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Soliton

A soliton is a stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one another emerge unmodified). Solitons were named by Zabusky and Kruskal (1965), and first appeared in the solution of the Korteweg-de Vries equation.

See also

Korteweg-de Vries Equation, Lax Pair, Sine-Gordon Equation

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References

Bullough, R. K. and Caudrey, P. J. (Eds.). Solitons. Berlin: Springer-Verlag, 1980.Dodd, R. K.; Eilbeck, J. C.; and Morris, H. C. Solitons and Nonlinear Equations. London: Academic Press, 1984.Drazin, P. G. and Johnson, R. S. Solitons: An Introduction. Cambridge, England: Cambridge University Press, 1988.Filippov, A. The Versatile Solitons. Boston, MA: Birkhäuser, 1996.Gu, C. H. Soliton Theory and Its Applications. New York: Springer-Verlag, 1995.Infeld, E. and Rowlands, G. Nonlinear Waves, Solitons, and Chaos, 2nd ed. Cambridge, England: Cambridge University Press, 2000.Lamb, G. L. Jr. Elements of Soliton Theory. New York: Wiley, 1980.Makhankov, V. G.; Fedyann, V. K.; and Pashaev, O. K. (Eds.). Solitons and Applications. Singapore: World Scientific, 1990.Newell, A. C. Solitons in Mathematics and Physics. Philadelphia, PA: SIAM, 1985.Olver, P. J. and Sattinger, D. H. (Eds.). Solitons in Physics, Mathematics, and Nonlinear Optics. New York: Springer-Verlag, 1990.Remoissent, M. Waves Called Solitons, 2nd ed. New York: Springer-Verlag, 1996.Russell, J. S. "Report on Waves." Report of the 14th Meeting of the British Association for the Advancement of Science. London: Jon Murray, pp. 311-390, 1844.Weisstein, E. W. "Books about Solitons." http://www.ericweisstein.com/encyclopedias/books/Solitons.html.Zabusky, N. J. and Kruskal, M. D. "Interaction of Solitons in a Collisionless Plasma and the Recurrence of Initial States." Phys. Rev. Let. 15, 240-243, 1965.

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Soliton

Cite this as:

Weisstein, Eric W. "Soliton." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Soliton.html

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