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Interaction of solitary waves for the generalized KdV equation. (English) Zbl 1247.35131

Summary: We consider a class of generalized KdV equations with a small parameter and nonlinearities of the type \(u^{m}\). We create a finite differences scheme to simulate the solution of the Cauchy problem and present some numerical results for the problem of the solitary waves interaction. In particular, we consider sufficient condition under which pairs of solitary waves interact, in the asymptotic sense, in accordance with the soliton scenario.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35C08 Soliton solutions

Software:

MACSYMA
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Full Text: DOI

References:

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