# Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation

## TL;DR

This paper constructs explicit solitary wave and Jacobi elliptic solutions for the generalized Benjamin-Bona-Mahony equation with various nonlinearities using the F-expansion method, enabling better control and simulation of physical systems.

## Contribution

It introduces a systematic method to derive exact wave solutions for a nonlinear PDE with arbitrary power-law nonlinearities, expanding the solution space for this equation.

## Key findings

- Explicit bright, dark, and antikink solitary wave solutions were obtained.
- Jacobi elliptic function solutions were derived for the equation.
- Solutions include fractional and integer power-law nonlinearities with multiple free parameters.

## Abstract

Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.