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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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