Research On High-Order Generalized Heisenberg Supermagnetic Models

The Heisenberg ferromagnet model is a significant integrable system.It describes that ferromagnetic material the nature of magnetization,and the relationship between magnetization and temperature change is presented.It is widely used in various fields in mathematics and physics.The generalization of integrable systems have also been studied,for instance,supersymmetric forms and multicomponent forms.In this paper,both generalized Heisenberg supermagnetic model and Z_n-Heisenberg ferromagnet model can be considered as extensions of Heisenberg ferromagnet model.As important integrable models,the generalized Heisenberg supermagnetic model and Z_n-Heisenberg ferromagnet model are gauge equivalent to supersymmetric nonlinear Schr(?)dinger equations and Z_n-nonlinear Schr(?)dinger equations,respectively.There are two research objects in this paper:one is the high-order generalized Heisenberg super-magnetic models,the other is the Z_n-Heisenberg ferromagnet model.Firstly,using the integrability condition,we construct the fifth-order generalized Heisenberg supermagnetic model and also investigate structure and properties of the supersymmetric systems.Moreover,the super fifth-order and the feimionic nonlinear Schr(?)dinger equations are established by gauge transformation with two square quadratic constraints.Secondly,the Z_n-nonlinear Schr(?)dinger equations and the Z_n-Heisenberg ferromagnet model are constructed and proved that they are gauge equivalent to each other.Finally,the practical significance and application of their are demonstrated and analyzed.