A5061265249- Nonlinear Waves and Solitons
- Algebraic structures and combinatorial models
- Advanced Topics in Algebra
- Nonlinear Photonic Systems
- Matrix Theory and Algorithms
- Black Holes and Theoretical Physics
- Quantum Mechanics and Non-Hermitian Physics
- Biological Activity of Diterpenoids and Biflavonoids
- Molecular spectroscopy and chirality
- Numerical methods for differential equations
- Algebraic and Geometric Analysis
- Advanced Fiber Laser Technologies
- Advanced Algebra and Geometry
- Holomorphic and Operator Theory
Henan University
2006-2023
Capital Normal University
2011-2018
Inner Mongolia University
2018
Dalian University of Technology
2018
Shandong Academy of Sciences
2018
Qilu University of Technology
2018
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.
We construct the W1+∞ 3-algebra and investigate its connection with integrable systems. Since a fixed generator W00 in operator Nambu 3-bracket recovers algebra, it is intrinsically related to KP hierarchy. For general case of 3-algebra, we directly derive KdV equations from Nambu–Poisson evolution equation different Hamiltonian pairs Due involves two Hamiltonians, deep relationship between hierarchy revealed. Furthermore give realization terms complex bosonic field. Based on 3-brackets...
In this paper, we first construct an integrable system whose solutions include the orthogonal Schur functions and symplectic functions.We find that can be obtained by one kind of Boson-Fermion correspondence which is slightly different from classical one.Then, a universal character satisfies bilinear equation new infinite-dimensional UC hierarchy.
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.
In terms of a 3-Lie algebra and the classical Poisson bracket {Bn,L} dKP hierarchy, special 3-bracket {Bm,Bn,L} is proposed. When m = 0 or 1, 3-lax equation ∂L∂t={Bm,Bn,L} hierarchy corresponding proof given. Meanwhile, for generalized case (m,n), also investigated.
Based on the Lax pair [Formula: see text] of mKP hierarchy and operator Nambu 3-bracket, we propose generalized equation with respect to triple text]. For different pairs in equation, a including is derived.
We construct the $W_{1+\infty}$ 3-algebra and investigate relation between this infinite-dimensional integrable systems. Since with a fixed generator $W^0_0$ in operator Nambu 3-bracket recovers algebra, it is natural to derive KP hierarchy from Nambu-Poisson evolution equation. For general case of 3-algebra, we directly KdV equations equation different Hamiltonian pairs. also discuss connection dispersionless equations. Due involves two Hamiltonians, deep relationship pairs revealed....