Exact solutions of equal-width equation and its conservation laws

Abstract

In this work we investigate the equal-width equation, which is used for simulation of (1-D) wave propagation in non-linear medium with dispersion process. Firstly, Lie symmetries are determined and then used to establish an optimal system of one-dimensional subalgebras. Thereafter with its aid we perform symmetry reductions and compute new invariant solutions, which are snoidal and cnoidal waves. Additionally, the conservation laws for the aforementioned equation are established by invoking multiplier method and Noether’s theorem.

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

“…It provides the most effective and powerful techniques for obtaining closed-form solutions to NPDEs. For example, see [26][27][28][29][30][31][32][33]. It is worth noting here that the notion of a Galois group had influenced Lie's work on differential equations (DEs).…”

An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation

“…Conserved quantities are a subject of keen interest in the fields such as theoretical and quantum mechanics [15,16,[28][29][30][31][32][33][34][35][36][37][38]. In isolated systems, energy, mass, charge, linear and angular momentum are conserved.…”