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Method for solving the Korteweg-de Vries equation. (English) Zbl 1103.35360
Summary: A method for solving the initial-value problem of the Korteweg-de Vries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as \(|x|\to\infty\). The method can be used to predict exactly the ”solitons”, or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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