Behavior of the wave solutions under the effect of the nonlinearity

Abstract

This work aims to determine the behavior of wave solution under the effect of nonlinearity with the contribution of the homogeneous balance principle and analysis methods. In the first step we studied the nonlinear atomic lattice equation via the coth and coth-csch methods. Eight new travelling wave solutions have been obtained. In the same context, the method of fractional transformations is introduced and which has provided various exact solutions. In the second step we applied the functional variable method to a set of nonlinear BBM equations of constant coefficients and the general equation Kdv-mKdv of variable coefficients.