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New solitary solutions with compact support for Boussinesq-like \(B(2n, 2n)\) equations with fully nonlinear dispersion. (English) Zbl 1139.35091
Summary: The Boussinesq-like equations \(B(2n, 2n)\) with fully nonlinear dispersion: \(u_{tt} + (u^{2n})_{xx} + (u^{2n})_{xxxx} = 0\), which exhibit compactons, i.e., solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case \(B\)(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in \(B(2n, 2n)\) equations. General formulas for the solutions of \(B(2n, 2n)\) equations are established.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C10 Series solutions to PDEs
35A25 Other special methods applied to PDEs
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