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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:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations