40685 - 812 the Supersymmetric Two Boson Hierarchies
نویسنده
چکیده
We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to the supersymmetric nonlinear Schrödinger equation without any arbitrary parameter which is known to be in-tegrable. We show that this supersymmetric system has three local Hamiltonian structures just like the bosonic counterpart and we show how the supersymmetric KdV equation can be embedded into this system.
منابع مشابه
ar X iv : s ol v - in t / 9 70 80 05 v 1 1 4 A ug 1 99 7 On the Integrable Hierarchies
A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N = 2 super Wn algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulted hierarchy contains the N = 2 super Virasoro algebra as a proper subalgebra. The simplest cases are discussed in detail. In particular, it is proved that the supersymm...
متن کاملar X iv : s ol v - in t / 9 71 20 09 v 1 1 8 D ec 1 99 7 Canonical Gauge Equivalences of the sAKNS and sTB
We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which turns out to be canonical. We also obtain the Darboux-Bäcklund transformations for the sAKNS hierarchy from these gauge transformations.
متن کاملBi - Hamiltonian Structure of the Supersymmetric Nonlinear Schrödinger Equation
We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two b...
متن کاملar X iv : h ep - t h / 92 11 01 4 v 1 3 N ov 1 99 2 UR – 1284 ER – 40685 – 734 SELF - DUALITY AND THE SUPERSYMMETRIC KdV HIERARCHY
We show how the supersymmetric KdV equation can be obtained from the self–duality condition on Yang–Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self–duality cond...
متن کاملThe Supersymmetric Two Boson Hierarchy
We summarize all the known properties of the supersymmetric integrable Two Boson equation. We present its nonstandard Lax formulation and tri-Hamiltonian structure, its reduction to the supersymmetric nonlinear Schrödinger equation and the local as well as nonlocal conserved charges. We also present the algebra of the conserved charges and identify its second Hamiltonian structure with the twis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994