Solutions and conservation laws of MEW-Burgers and KdV-BBM equations

Abstract

In this work we study two nonlinear partial differential equations of fluid mechanics. The Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the t~o-way propagation of waves, is studied first. We compute the optimal system of one-dimensional sub-algebras and use it to perform symmetry reductions and find group-invariant solutions. Also, we derive conservation laws of the KdV-BBM equation using the multiplier approach. Secondly we study the modified equal width Burgers equation, which describes long wave propagation in nonlinear media with dispersion and dissipation. We construct exact solutions using its Lie point symmetries and invoking the ( G' / G)-expansion method. Moreover we determine the conservation laws by employing the new conservation theorem due to Ibragimov.