On the Generalized Heisenberg Supermagnetic Model

In this paper, we construct the generalized Heisenberg supermagnetic models with two different constraints and investigate the integrability of the super integrable systems. By virtue of the gauge transformation, their corresponding gauge equivalent counterparts are derived, i.e., the super and fermionic mixed derivative nonlinear Schrödinger equations, respectively.     

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters. The boson-fermion correspondence for these symmetric functions have been presented. In virtue of quantum fields, we derive a series of infinite order nonlinear integrable equations, namely, universal character hierarchy, symplectic KP hierarchy and symplectic universal character hierarchy, respectively. In addition, the solutions of these integrable systems have been discussed.     

Integrable Deformations of Heisenberg Supermagnetic Model

We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic 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））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.     

Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model

We construct the fourth-order inhomogeneous generalized HS model and investigate the integrability property of the supersymmetric integrable system. Moreover, in terms of the gauge transformation, we investigate the corresponding gauge equivalent counterparts under two constraints, i.e., the super inhomogeneous generalized nonlinear Schr?dinger equation and the fermionic inhomogeneous generalized nonlinear Schr?dinger equation.