Two Similarity Reductions and New Solutions for the Generalized Variable-Coefficient KdV Equation by Using Symmetry Group Method

TL;DR

This paper applies symmetry group analysis to a generalized variable-coefficient KdV equation, deriving new solutions and identifying admissible coefficient forms through symmetry reductions.

Contribution

It introduces a systematic symmetry analysis approach to find new solutions for the generalized variable-coefficient KdV equation.

Findings

Two symmetry generators identified.

New exact solutions obtained for the generalized vcKdV.

Admissible coefficient forms determined.

Abstract

In this paper, a generalized variable-coefficient KdV equation (vcKdV) arising in fluid mechanics, plasma physics and ocean dynamics is investigated by using symmetry group analysis. Two basic generators are determined, and for every generator in the optimal system the admissible forms of the coefficients and the corresponding reduced ordinary differential equation are obtained. The search for solutions to those reduced ordinary differential equations yields many new solutions for the generalized vcKdV equation.