New Complexiton Solutions of the KdV and Coupled KdV Equations

TL;DR

This paper introduces a new method to find complexiton solutions for the KdV and coupled KdV equations, expanding the set of known solutions for these nonlinear PDEs.

Contribution

A novel double-sub equation method is developed and applied to derive new complexiton solutions for the KdV and coupled KdV equations.

Findings

New complexiton solutions for KdV and coupled KdV equations

Graphical illustrations of the solutions

Method demonstrates effectiveness in solving nonlinear PDEs

Abstract

A new approach to double-sub equation method is introduced to construct novel solutions for the nonlinear partial differential equations. It is applied to the Korteweg-de Vries (KdV) equation and yields new complexiton solutions of both the KdV and coupled KdV equations. The graphs of the solutions are also illustrated.