On optimal system, exact solutions and conservation laws of the modified equal-width equation

Abstract

In this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two different methods, the multiplier method and Noether approach.

Keywords

• modified equal-width equation
• lie symmetries
• optimal system of one-dimensional subalgebras
• cnoidal and snoidal waves
• conservation laws
• 35c07
• 35l65