Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

Author:

Seadawy Aly R.12

Affiliation:

1. Mathematics Department, Faculty of Science, Taibah University, Saudi Arabia

2. Mathematics Department, Faculty of Science, Beni-Suef University, Egypt

Abstract

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Mathematics,Computer Science (miscellaneous)

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