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Integral approach to compacton solutions of Boussinesq-like $$B$$($$m$$,$$n$$) equation with fully nonlinear dispersion. (English) Zbl 1068.35135
Summary: There exists much good work in the area of usual solitons, but there appears little in the field of compacton solutions. Only a few mathematical tools were employed so far. Recently, Z. Yan [Chaos Solitons Fractals 14, No. 8, 1151–1158 (2002; Zbl 1038.35082)] extended the decomposition method to seek compacton solutions of $$B(m,n)$$ equation $$u_{tt}=(u^n)_{xx}+(u^m)_{xxx}$$. We present a different approach, integral approach, to investigate the compacton solutions of the $$B(m,n)$$ equation. Not only Yan’s results but also many new compacton solutions of the $$B(m,n)$$ equation are obtained. Our approach is simple and also suitable for studying compacton solutions of some other equations.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations
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