Explicit and exact special solutions for BBM-like B(m, n) equations with fully nonlinear dispersion

In this paper, the BBM-like equations with fully nonlinear dispersion, B(m, n) equations: ut + (um)x − (un)xxt = 0 which exhibit solutions with compact support and with solitary patterns, are studied. The exact solitary-wave solutions with compact support and exact special solutions with solitary patterns of the equations are found by a new method. The special cases, B(2, 2) and B(3, 3), are used to illustrate the concrete scheme of our approach presented by this paper 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.