Odd Bihamiltonian Structure of New Supersymmetric N=2,4 KdV And Odd SUSY Virasoro - Like Algebra

TL;DR

This paper develops a method for supersymmetrizing soliton equations with odd Hamiltonian structures, introduces new supersymmetric N=2,4 KdV equations, and reveals their connection to an odd SUSY Virasoro-like algebra.

Contribution

It presents a novel supersymmetrization approach for soliton equations with odd Hamiltonian structures and introduces new N=2,4 SUSY KdV equations with associated algebraic structures.

Findings

New supersymmetric N=2,4 KdV equations introduced

Second odd Hamiltonian operator generates SUSY Virasoro-like algebra

Method establishes supersymmetrization of soliton equations with odd structures

Abstract

The general method of the supersymmetrization of the soliton equations with the odd (bi) hamiltonian structure is established. New version of the supersymmetric N=2,4 (Modified) Korteweg de Vries equation is given, as an example. The second odd Hamiltonian operator of the SUSY KdV equation generates the odd N=2,4 SUSY Virasoro - like algebra.