Odd Hamiltonian Structure for Supersymmetric Sawada - Kotera Equation

TL;DR

This paper investigates the odd Hamiltonian structure of the supersymmetric Sawada-Kotera equation, demonstrating its integrability through a bi-Hamiltonian framework involving both quadratic and cubic operators.

Contribution

It introduces an odd bi-Hamiltonian structure for the supersymmetric Sawada-Kotera equation, establishing its integrability and connecting physical and exotic equations via Hamiltonian operators.

Findings

The supersymmetric Sawada-Kotera equation has a bi-Hamiltonian structure.

The product of symplectic and implectic operators yields the recursion operator.

The equation's integrability is confirmed through its bi-Hamiltonian formulation.

Abstract

We study the supersymmetric N=1 hierarchy connected with the Lax operator of the supersymmetric Sawada-Kotera equation. This operator produces the physical equations as well as the exotic equations with odd time. The odd Bi-Hamiltonian structure for the N=1 Supersymmetric Sawada - Kotera equation is defined. The product of the symplectic and implectic Hamiltonian operator gives us the recursion operator. In that way we prove the integrability of the supersymmetric Sawada - Kotera equation in the sense that it has the Bi-Hamiltonian structure. The so called "quadratic" Hamiltonian operator of even order generates the exotic equations while the "cubic" odd Hamiltonian operator generates the physical equations.