Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations

TL;DR

This paper introduces a novel method using factorization techniques to find explicit traveling wave solutions of the perturbed KdV equation, applicable when certain coefficient conditions are met, enhancing solution strategies for nonlinear PDEs.

Contribution

The paper presents a new two-step factorization approach to derive explicit solutions of the perturbed KdV equation under specific coefficient conditions.

Findings

Derived explicit traveling wave solutions using factorization methods.

Reduced the perturbed KdV to nonlinear second order and Bernoulli/Abel equations.

Solutions expressed in terms of exponential and Weierstrass functions.

Abstract

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential and Weierstrass functions