New families of solitons with compact support for Boussinesq-like B(m,n) equations with fully nonlinear dispersion

Studying special solitons with compact support is of important significance in soliton theory. There exists much good work in the area of usual solitons, but there appears very little in the way of compacton solutions. In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(m,n) equations, utt=(un)xx+(um)xxxx, which was introduced by us to understand the role of nonlinear dispersion in pattern formation [Z.Y. Yan, Commun. Theor. Phys. 36 (2001) 385], are investigated again. New soliton solutions with compact support are found which have the remarkable properties: They collide elastically, but unlike the usual solitons, they have compact support. With the aid of Maple, the two special cases, B(2,2) equation and B(3,3) equation, are chosen to illustrate the concrete scheme of the decomposition method in B(m,n) equation. In addition, two new general compacton solutions of B(m,m) equation are also found.