Application of the modified method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg - de Vries equation and generalized Camassa-Holm equation

TL;DR

This paper applies a modified method of simplest equations to derive exact traveling-wave solutions for the extended Korteweg-de Vries and generalized Camassa-Holm equations, revealing solutions relevant to surface water waves.

Contribution

It introduces a modified method of simplest equations to find exact solutions for two complex nonlinear PDEs, expanding analytical tools for wave modeling.

Findings

Exact solutions for extended KdV and Camassa-Holm equations obtained

Solutions include those corresponding to surface water waves

Use of Bernoulli, Riccati, and extended tanh equations as simplest equations

Abstract

The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh - equation are used as simplest equations. Some of the obtained solutions correspond to surface water waves.