The Super W_3 Conformal Algebra and the Boussinesq Hierarchy

TL;DR

This paper establishes the bihamiltonian structure of the N=2 supersymmetric Boussinesq equation, demonstrating its integrability and highlighting its pure supersymmetric effects distinct from classical counterparts.

Contribution

It explicitly constructs the Lax pair for the supersymmetric Boussinesq equation and proves its integrability, revealing a unique supersymmetric structure not reducible to classical forms.

Findings

Bihamiltonian structure of N=2 supersymmetric Boussinesq equation identified

Lax pair explicitly constructed for the supersymmetric equation

Proves the integrability of the supersymmetric Boussinesq equation

Abstract

The bihamiltonian structure of the N=2 Supersymmetric Boussinesq equation is found. It is not reduced to the corresponding classical structure and hence it describes the pure supersymmetric effect. For the supersymmetric Boussinesq equation which contains the classical partner the Lax pair is given explicitly. Thus we prove the integrability of the equation.