Lie symmetry analysis and exact solutions for a variable coefficient Gardner equation arising in arterial mechanics

TL;DR

This paper applies symmetry analysis and elliptic function methods to find new exact solutions for a variable-coefficient Gardner equation relevant in arterial mechanics.

Contribution

It introduces a novel combination of symmetry analysis and Jacobi elliptic function expansion to solve the variable-coefficient Gardner equation.

Findings

Derived new exact solutions for the PDE

Identified symmetries of the variable-coefficient Gardner equation

Enhanced understanding of solutions in arterial mechanics context

Abstract

In this paper, a variable-coefficient Gardner equation is considered. By using the classical symmetry analysis method symmetries for this equation are obtained. Then, the generalized Jacobi elliptic function expansion method is used to solve the reduced ODE. Some new exact solutions for the considered PDE are obtained.