Solitary wave solutions for nonlinear partial differential equations containing monomials of odd and even grades with respect to participating derivatives

TL;DR

This paper develops a method to find exact solitary wave solutions for nonlinear PDEs with monomials of both odd and even grades, demonstrating its effectiveness through various examples.

Contribution

It introduces a systematic approach using the simplest equation method for solving nonlinear PDEs with mixed-grade monomials, including special cases with only odd or even grades.

Findings

Successfully derived solitary wave solutions for complex nonlinear PDEs.

Demonstrated the method's applicability through multiple illustrative examples.

Provided a unified framework for equations with different monomial grades.

Abstract

We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider first the general case of presence of monomials of the both (odd and even) grades and then turn to the two particular cases of nonlinear equations that contain only monomials of odd grade or only monomials of even grade. The methodology is illustrated by numerous examples.