Lie Symmetry Classification and Numerical Analysis of KdV Equation with Power-law Nonlinearity

TL;DR

This paper performs a Lie symmetry analysis of the KdV equation with power-law nonlinearity, derives invariant and exact solutions, classifies the Lie algebra, and employs a Chebyshev pseudo-spectral method for numerical validation.

Contribution

It provides a comprehensive symmetry classification and exact solutions for the KdV equation with power-law nonlinearity, combined with a numerical analysis using CPSM.

Findings

Derivation of invariant and exact solutions from Lie symmetries

Classification of the Lie algebra and optimal system

Numerical validation using Chebyshev pseudo-spectral method

Abstract

In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie algebraic classifications and the optimal system are discussed. Finally, using Chebyshev pseudo-spectral method (CPSM), a numerical analysis to solve the invariant solutions corresponded the Lie symmetries of main equation is presented. This method applies the Chebyshev-Gauss-Lobatto points as collocation points.