On exact solutions, conservation laws and invariant analysis of the generalized Rosenau-Hyman equation

TL;DR

This paper investigates the invariant properties, exact solutions, and conservation laws of a generalized Rosenau-Hyman equation with variable coefficients using Lie and nonclassical symmetry methods, providing new analytical solutions and conservation laws.

Contribution

It introduces a comprehensive symmetry analysis and derives new exact solutions and conservation laws for the generalized Rosenau-Hyman equation with time-dependent coefficients.

Findings

Derived symmetries using Lie and nonclassical methods

Obtained exact solutions and visualized them graphically

Constructed local conservation laws via multiplier approach

Abstract

In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for investigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive symmetries admitted by considered equation. Symmetry reductions are performed for each components of optimal set. Also nonclassical approach is employed on considered equation to find some additional supplementary symmetries and corresponding symmetry reductions are performed. Later three kinds of exact solutions of considered equation are presented graphically for different parameters. In addition, local conservation laws are constructed for considered equation by multiplier approach.