N = 2 SUPER W₃ ALGEBRA AND N = 2 SUPER BOUSSINESQ EQUATIONS

Abstract

We study classical N=2 super W3 algebra and its interplay with N=2 supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs-covariant reduction approach. These techniques have been previously used by us in the bosonic W3 case to give a new geometric interpretation of the Boussinesq hierarchy. Here we deduce the most general N=2 super Boussinesq equation and two kinds of the modified N=2 super Boussinesq equations, as well as the super Miura maps relating these systems to each other, by applying the covariant reduction to certain coset manifolds of linear [Formula: see text] symmetry associated with N=2 super W3. We discuss the integrability properties of the equations obtained and their correspondence with the formulation based on the notion of the second Hamiltonian structure.

N = 2 KP and KdV Hierarchies in Extended Superspace

“…There has been recently an important activity in the study of N = 2 supersymmetric hierarchies (KP [1,2,3,4,6], generalizations of KdV [5,7], Two Bosons [8], NLS [9,10,11], etc..). The most usual tools in this field are the algebra of N = 1 pseudo-differential operators and Gelfand-Dickey type Poisson brackets [12].…”

BRST charges for finite nonlinear algebras

“…For a 3 /a 2 = −16 or a 3 /a 2 = −1/4 this algebra is a finite dimensional "cut" of the bosonic part of the N = 2 super W 3 algebra [13] …”

A two-component generalization of the Degasperis–Procesi equation

“…Let us first consider the decompression for the degenerated case where λ = 0, c = −2 and z = m. We make the following assumptions on the entries of the Γ matrix Γ 1,1 = J 1,1 , Γ 1,2 = J 1,2 , Γ 2,1 = J 2,1 where J 1,1 , J 1,2 , J 2,1 are defined in eq. (23). For the rest elements we assumed that they are constructed out of the function ρ its derivatives and differential operators in such a way that they reduces to 0 when ρ = 0.…”

“…The N = 2 supersymmetric Boussinesq equation has been constructed utilizing the N = 2 supersymmetric extension of the W 3 algebra [22,23]. This supersymmetric algebra is generated by two N = 2 supermultiplets, with the conformal spins (1, 3 2 , 3 2 , 2) and (2, 5 2 , 5 2 , 3) and exists at an arbitrary value of the central charge and is connected with the following supersymmetric matrix operator Ĵ with the entries…”