Explicit travelling wave solutions of variants of the K(n,n) and the ZK(n,n) equations with compact and noncompact structures

Abstract

In this work two powerful schemes, that use the reliable ideas of the sine-cosine method and the tanh method, are presented. Variants of the K(n,n) and the ZK(n,n) are selected to illustrate the two methods and to derive compact and noncompact solutions for these nonlinear variants with dispersive effects. The coefficients of the derivatives of the equation play a major role in change of the physical structures of the solutions.