Darboux Wronskian solutions of Ito typed coupled KdV equation with exact solitonic solutions and conserved densities

TL;DR

This paper derives Darboux and Wronskian solutions for the Ito-type coupled KdV equation, providing explicit multi-solitonic solutions and conserved densities, advancing analytical methods for integrable systems.

Contribution

It introduces generalized N-fold Darboux transformations and exact multi-solitonic solutions for the coupled KdV system, along with conserved densities derived via Riccati equations.

Findings

Explicit Darboux solutions for the Ito coupled KdV equation.

Generalized N-fold Darboux transformations using Wronskians.

Derivation of conserved densities and continuity equations.

Abstract

In this article, we derive the Darboux solutions of Ito type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. Then we generalise $N$-fold Darboux transformations in terms of Wronskians. We also derive the exact multi-solitonic solutions for the coupled field variables of that system in the background of zero seed solutions. The last section encloses the derivation of continuity equation with several conserved densities through its Riccati equation.