Abstract This paper is concerned with the construction of two types generalized Heisenberg supermagnetic models constraint S^3=S, including inhomogeneous supermagnet model in (1+1)-dimensional and $(2+1)$-dimensional model. Furthermore, by means gauge transformation, we investigate equivalent counterparts, which are nonlinear Schr"odinger equation (2+1)-dimensional super equation, respectively.

Abstract In this paper, we investigate the super mixed derivative nonlinear Schrödinger (super MDNLS) equation by means of fermionic prolongation structure approach. Based upon representations algebra, present Lax representation and Bäcklund transformation MDNLS equation.

The Heisenberg supermagnet models which can be regarded as the superextensions of ferromagnet model are important supersymmetric (1+1)-dimensional integrable systems. We investigate their integrability in higher dimensions and construct (2+1)-dimensional with respect to two different quadratic constraints superspin variable. By means gauge transformation, we derive equivalent counterparts, i.e., Grassman odd super nonlinear Schrödinger equation, respectively.

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 higher order deformations of models two different constraints: (i) S2=3S−2I for S∊USPL(2/1)/S(U(2)×U(1)) (ii) S2=S S∊USPL(2/1)/S(L(1/1)×U(1)). terms gauge transformation, their corresponding equivalent counterparts are derived.

Based on the covariant prolongation structure technique, we construct integrable higher-order deformations of (2+1)-dimensional Heisenberg ferromagnet model and obtain their su(2) × R(λ) structures. By associating these deformed multidimensional models with moving space curve in Euclidean using Hasimoto function, derive geometrical equivalent counterparts, i.e., nonlinear Schrodinger equations.

We construct the integrable deformations of Heisenberg supermagnet model with quadratic constraints (i) S2 = 3S − 2I, for S ∊ USPL(2/1)/S(U(2) × U(1)) and (ii) S, USPL(2/1)/S(L(1/1) U(1)). Under gauge transformation, their corresponding equivalent counterparts are derived. They Grassman odd super mixed derivative nonlinear Schrödinger equation, respectively.

The fermionic covariant prolongation structure theory is investigated. We extend the technique to multidimensional super nonlinear evolution equation and present fundamental equations determining structure. Furthermore, we investigate a (2+1)-dimensional Schrödinger analyze its integrability by means of this technique. derive Lax representation Bäcklund transformation. Moreover, solution integrable equation.

In this paper, we propose two types of universal characters corresponding to partition shapes π = (3) and (2, 1) construct their vertex operators realizations. It is proved that (3)-type 1)-type can be derived by the products acting on identity. Furthermore, investigate means Hamiltonian fermions expectation values. addition, based upon bilinear equations, present hierarchies whose τ functions from characters.

The q-deformation of the infinite-dimensional n-algebras is investigated. Based on structure q-deformed Virasoro–Witt algebra, we derive a nontrivial n-algebra which nothing but sh-n-Lie algebra. Furthermore in terms pseud-differential operators, construct (co)sine and SDiff(T2) n-algebra. We find that they are algebras for n even case. In magnetic translation an explicit physical realization given.

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

Abstract The Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional models with quadratic constraints and investigate integrability systems. In terms gage transformation, we derive their equivalent counterparts. Furthermore, also new solutions systems by means Bäcklund transformations.

The Heisenberg supermagnet model which is the supersymmetric generalization of ferromagnet an important integrable system.We consider deformations under two constraint 1. S 2 = for ∈ USPL(2/1)/S(L(1/1) × U(1)) and 2. 3S -2I USPL(2/1)/S(U(2) U(1)).By means gauge transformation, we construct equivalent counterparts, i.e., super generalized Hirota equation Gramman odd nonlinear Schrödinger equation.

We present the W1+∞ constraints for Gaussian Hermitian matrix model, where constructed constraint operators yield n-algebra. For Virasoro constraints, we note that give null 3-algebra. With help of our derive a new effective formula correlators in model.

We construct the multi-variable realizations of W1+∞ algebra such that they lead to n-algebra. Based on our algebra, we derive constraints for hermitian one-matrix model. The constraint operators yield not only but also closed

The generalized additional symmetries of the two-Toda lattice hierarchy are investigated in this paper. algebraic structure symmetry is showed as w∞⊗w∞. And actions on τ-function also discussed, by restricting to semi-infinite case.