New solitary wave solutions with compact support for the KdV-like K(m, n) equations with fully nonlinear dispersion

In this paper, a new method different from the Adomian decomposition method, namely, the extend sine–cosine method, is proposed, to investigate the compacton solutions of the KdV-like equations with fully nonlinear dispersion, K(m, n) equations: ut + (um)x + (un)xxx = 0. The new exact solitary-wave solutions with compact support of the equations are found by our new method. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete scheme of our approach in K(m, n) equations. An entirely new general formulas for the solutions of K(m, n) equations for all types where m = n are established. Our results include not only some known results in literature as special cases but also some new exact special solutions. The method presented by this paper is suitable for studying compacton solutions of some other equations.