Traveling wave solutions of the generalized scale-invariant analogue of the KdV equation by tanh-coth method

TL;DR

This paper introduces a new approach using the tanh-coth method to find traveling wave solutions of the generalized scale-invariant KdV equation, revealing multiple solution families and demonstrating the method's effectiveness.

Contribution

First application of the tanh-coth method to the generalized scale-invariant KdV equation, providing new solutions and validating the technique's utility in nonlinear differential equations.

Findings

Multiple families of bell-shaped solutions identified

The tanh-coth method proved effective for this class of equations

The approach can be applied to other nonlinear problems

Abstract

In this work, the generalized scale-invariant analogue of the Korteweg-de Vries (gsiaKdV) equation is studied. For the first time, the tanh-coth methodology is used to find traveling wave solutions for this nonlinear equation. The considered generalized equation is a connection between the well-known KdV equation and the recently investigated SIdV equation. The obtained results show many families of solutions for the model, indicating that this equation also shares bell-shaped solutions with KdV and SIdV, as previously documented by other researchers. Finally, by executing the symbolic computation, we demonstrate that the employed technique is a valuable and effective mathematical tool that can be used to solve problems that arise in the cross-disciplinary nonlinear sciences and applied mathematics.