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Shock-peakon and shock-compacton solutions for \(K(p,q)\) equation by variational iteration method. (English) Zbl 1119.65099

Summary: By the variational iteration method, we obtain new solitary solutions for nonlinear dispersive equations. Particularly, shock-peakon solutions in the \(K(2,2)\) equation and shock-compacton solutions in the \(K(3,3)\) equation are found by this simple method. These two types of solutions are new solitary wave solutions which have the shapes of shock solutions and compacton solutions (or peakon solutions).

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35L67 Shocks and singularities for hyperbolic equations
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