Integrable higher order deformations of Heisenberg supermagnetic model

Abstract

The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S2=3S−2I for S∊USPL(2/1)/S(U(2)×U(1)) and (ii) S2=S for S∊USPL(2/1)/S(L(1/1)×U(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.

Darboux transformations of the Supersymmetric BKP hierarchy

“…It has been demonstrated that there is a close relation between HS model and the strong electron correlated Hubbard model. Lately, various deformed integrable HS models were constructed and their integrability properties have been also studied [4,[21][22][23]. The aim of this paper is to establish another deformations of HS models, which, as far as these authors's knowledge goes, was not previously known.…”

On a supersymmetric nonlinear integrable equation in (2+1) dimensions

“…Since various techniques like Painlevé test [11], Darboux and Bäcklund transformations [6,8,19], Hirota bilinear method [7,13] and prolongation structure theory [15] have been extended to analysis supersymmetric integrable systems, a large number of (1+1)-dimensional integrable supersymmetric equations have been well studied, such as supersymmetric Korteweg-de Vries equation [5,12], supersymmetric Kadomtsev-Petviashvili hierarchy [10,18], supersymmetric nonlinear Schrödinger equation [14] and Heisenberg supermagnet model [4,9,21].…”

On the Higher-Order Inhomogeneous Heisenberg Supermagnetic Models

“…The HF model has been well developed and it is geometrical and gauge equivalent to the nonlinear Schrödinger equation (NLSE) [3,4]. There have been extensive study and application of the HF models and the inhomogeneous integrable equations [5,6], such as deformed HF model [7,8], extended high-order HF model [9][10][11], inhomogeneous deformed HF model [3,12], the multidimensional HF model [13,14], the multi-component extended HF model [15], and integrable counterparts of the Heisenberg soliton hierarchy [16].…”

“…The Heisenberg supermagnet (HS) model can be regarded as the supersymmetric extension of the HF model [11,25]. The HS models and their corresponding gauge equivalence were first developed by Makhankov et al [25].…”

“…Furthermore, the higher order and inhomogeneous HS models have been discussed and their integrable structure and properties have been also derived. Meanwhile, the authors [11,30] constructed the third-order, fourth-order and fifth-order generalized HS models from which their gauge equivalent equations have been presented. Moreover, Yan et al developed the inhomogeneous thirdorder and fourth-order generalized HS models [26,27], respectively.…”