Soliton solution of the generalized fifth order Hirota-Satsuma equation coupled with KdV

TL;DR

This paper introduces a fifth-order PDE generalizing the Hirota-Satsuma coupled with KdV system, and demonstrates the existence of soliton solutions using the tanh method and numerical analysis.

Contribution

It presents a new fifth-order PDE extension of the Hirota-Satsuma system and confirms soliton solutions through analytical and numerical methods.

Findings

The generalized equation admits soliton solutions.

Application of tanh method effectively transforms PDEs to ODEs.

Numerical solutions verify the soliton behavior.

Abstract

We introduced a fifth-order partial differential equation as a generalization of Hirota-Satsuma coupled with KdV system. This equation is investigated based on tanh method. By applying the suitable independent variable in Hirota-Satsuma equation, we can convert this partial differential equations(PDE) into ordinary differential equations(ODE) .Solving the converted Hirota-Satsuma equation by numerical methods we showed this equation have had soliton solution.