Exact special solutions with solitary patterns for Boussinesq-like B(m,n) equations with fully nonlinear dispersion

In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(m,n) equations: utt+(um)xx−(un)xxxx=0 which exhibit solutions with solitary patterns, are studied. New exact solitary solutions of the equations are found. 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. The nonlinear equations B(m,n) are addressed for two different cases, namely when m=n being odd and even integers. General formulas for the solutions of B(m,n) equations are established.