Exact solutions of the generalized $K(m,m)$ equations

TL;DR

This paper derives exact periodic wave solutions for a generalized family of nonlinear equations extending the $K(m,m)$ equation, providing new analytical insights into their behavior.

Contribution

It introduces a method to construct exact solutions for the generalized $K(m,m)$ equations, expanding understanding beyond the classical form.

Findings

Explicit periodic wave solutions are obtained.

The solutions generalize known results for the $K(m,m)$ equation.

The approach can be applied to other nonlinear equations.

Abstract

Family of equations, which is the generalization of the $K(m,m)$ equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed.