The Integrability of New Two-Component KdV Equation

TL;DR

This paper investigates the integrability of a new two-component KdV equation, establishing its bi-Hamiltonian structure, connection to supersymmetric hierarchies, and providing a Lax representation and Hamiltonian formulation.

Contribution

It introduces the bi-Hamiltonian and Lax structures of a newly identified two-component KdV equation, linking it to supersymmetric integrable systems.

Findings

Bi-Hamiltonian representation established

Connection to supersymmetric KP hierarchy demonstrated

Lax and Hamiltonian structures explicitly constructed

Abstract

We consider the bi-Hamiltonian representation of the two-component coupled KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov. Connection of this equation with the supersymmetric Kadomtsev-Petviashvilli-Radul-Manin hierarchy is presented. For this new supersymmetric equation the Lax representation and odd Hamiltonian structure is given.