Solitary wave solutions of several nonlinear PDEs modeling shallow water waves

TL;DR

This paper uses a modified method of simplest equations to find exact traveling wave solutions for nonlinear PDEs modeling shallow water waves, including viscous effects, and discusses boundary conditions.

Contribution

It introduces a novel application of the modified method of simplest equations using Riccati equations to solve shallow water wave PDEs.

Findings

Two exact traveling wave solutions obtained.

Discussion on boundary condition implementation.

Application to viscous fluid shallow water models.

Abstract

We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow water waves in viscous fluid (Topper-Kawahara equation). As simplest equation we use a version of the Riccati equation. We obtain two exact traveling wave solutions of equations from the studied class of equations and discuss the question of imposing boundary conditions on one of these solutions.