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Variational approach to solitons of nonlinear dispersive \(K(m, n)\) equations. (English) Zbl 1143.35361
Summary: Via He’s semi-inverse method, a variational principle is established for the nonlinear dispersive \(K(m, n)\) equations. Based on this formulation, a solitary solution can be easily obtained using Ritz method. The present paper provides a new approach to the search of wave solutions including solitions, compactons and periodic solutions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35A15 Variational methods applied to PDEs
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