New Two-Componet Coupled KdV Equation and its Connection with the Generalized Harry Dym Equation

TL;DR

This paper introduces a new integrable two-component coupled KdV system derived from Lax operators in the Dym hierarchy, establishing its connection with the generalized Harry Dym equation and providing its Lax and Hamiltonian structures.

Contribution

It presents a novel two-component coupled KdV system linked to the generalized Harry Dym equation, including its Lax representation and Hamiltonian structure.

Findings

Derived a new integrable two-component KdV system.

Connected the system with the generalized Harry Dym equation.

Established Lax and Hamiltonian structures for the system.

Abstract

It is shown that, two different Lax operators in the Dym hierarchy, produce two generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component KdV system. The first equation gives us new integrable two-component KdV system while the second reduces to the known symmetrical two-component KdV equation. For this new two-component coupled KdV system the Lax representation and Hamiltonian structure is defined.