Group analysis of Benjamin-Bona-Mahony equations with time dependent coefficients

TL;DR

This paper performs a comprehensive group classification of Benjamin-Bona-Mahony equations with time-dependent coefficients, identifying symmetries and equivalence transformations to facilitate understanding of their solutions.

Contribution

It provides a complete group classification of variable-coefficient BBM equations using two methods, including the derivation of a class with forcing terms.

Findings

Two lists of equations with Lie symmetry extensions are presented.

Complete group classification achieved via two different methods.

Derived classification includes equations with forcing terms.

Abstract

Group classification of a class of Benjamin-Bona-Mahony (BBM) equations with time dependent coefficients is carried out. Two equivalent lists of equations possessing Lie symmetry extensions are presented: up to point equivalence within the class of BBM equations and without the simplification by equivalence transformations. It is shown that the complete results can be achieved using either the gauging of arbitrary elements of the class by the equivalence transformations or the method of mapping between classes. As by-product of the second approach the complete group classification of a class of variable-coefficient BBM equations with forcing term is derived.