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A soliton is a non-linear object which moves through space without dispersion at constant speed. They occur naturally as solutions to the Korteweg - de Vries equation. They were first observed by John Scott Russell in the 19th century and then by Martin Kruskal and Norman Zabusky (who coined the term soliton) in a famous computer simulation in 1965. Insight into solitons can be obtained by noting that the Korteweg - de Vries equation satisfies D'Alembert's solution:
We see at once that this satisfies two important criteria: it has a constant velocity  , and it can also be shown that the two functions  and  can collide without altering shape. Solitons also occur in non-linear optics and as solutions to field equations in quantum field theory.
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"soliton" is owned by invisiblerhino.
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| Other names: |
solitary wave |
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Cross-references: quantum field theory, equations, field, occur in, functions, term, Korteweg - de Vries equation, solutions, object
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This is version 7 of soliton, born on 2008-02-11, modified 2008-03-16.
Object id is 10259, canonical name is Soliton.
Accessed 412 times total.
Classification:
| AMS MSC: | 35Q51 (Partial differential equations :: Equations of mathematical physics and other areas of application :: Solitons) | | | 37K40 (Dynamical systems and ergodic theory :: Infinite-dimensional Hamiltonian systems :: Soliton theory, asymptotic behavior of solutions) |
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Pending Errata and Addenda
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