Integral approach to compacton solutions of Boussinesq-like B(m,n) equation with fully nonlinear dispersion

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, Yan Chaos, Solitons & Fractals 14 (2002) 1151] extended the decomposition method to seek compacton solutions of B(m,n) equation u_tt=(uⁿ)_xx+(u^m)_xxxx. In this paper 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.