Group Analysis via Weak Symmetries For Benjamin-Bona-Mahony Equation

TL;DR

This paper investigates weak symmetries of the Benjamin-Bona-Mahony (BBM) equation using non-classical symmetries and classical symmetry algebra, leading to similarity reductions and exact solutions.

Contribution

It introduces a novel application of weak symmetry analysis to the BBM equation, deriving new similarity solutions and exact solutions.

Findings

Derived similarity reduced equations

Obtained exact solutions of the BBM equation

Applied non-classical symmetry methods

Abstract

In this paper, weak symmetries of the Benjamin-Bona-Mahony (BBM) equation have been investigated. Indeed, this method has been performed by applying the non-classical symmetries of the BBM equation and the infinitesimal generators of the classical symmetry algebra of the KdV equation as the starting constraints. Similarity reduced equations as well as some exact solutions of the BBM equation are obtained via this method.