Construction of exact solitary solutions for Boussinesq-like B(m, n) equations with fully nonlinear dispersion by the decomposition method

In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(m, n) equations: utt − (um)xx + (un)xxxx = 0, are investigated. Exact solitary solutions of the equations are obtained by using the decomposition method. The two special cases, B(2, 2) and B(3, 3), are chosen to illustrate the concrete scheme of the decomposition method in B(m, n) equations. General formulas for the solutions of B(m, n) equations are established.