Analysis of generalized BBM equations: Symmetry groups and conservation laws

Abstract

In this work we study a generalized BBM equation from the point of view of the theory of symmetry reductions in partial differential equations.We obtain the Lie symmetries, then we use the transformation groups to reduce the equations into ordinary differential equations. Physical interpretation of these reductions and some exact solutions are also provided. Local conservation laws are continuity equations that provide conserved quantities of physical importance for all solutions of a particular equation. In addition, the existence of an infinite hierarchy of local conservation laws of a partial differential equation is a strong indicator of its integrability. For any particular partial differential equation, a complete classification of all local low-order conservation laws can be derived by using the multiplier method.