Abstract
In this article, we study the nonlinear higher order of extended KdV equation with free surface displacement. The modified exponential rational function method is used in order to find exact solutions of the extended KdV equation. As a result, various exact solutions for the equation under consideration are obtained. To illustrate the graphical behavior of the results, some of the obtained solutions are presented graphically.
•The analytical and computational solutions are obtained.•The nonlinear extended KdV dynamical equation.•Nonlinear long internal waves in a stratified shear flow.•Weakly dispersive prorogation of waves structures.