Fajun Yu

A new matrix Lie algebra, the multicomponent Yang hierarchy and its super-integrable coupling system

Abstract A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A ∼ 2 M . It follows that an isospectral problem is established. By use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component Yang hierarchy is given. Finally, the multi-component super-integrable coupling system of Yang hierarchy is presented by enlarging matrix spectral problem.

An integrable couplings of Dirac soliton hierarchy with self-consistent sources

Abstract A kind of the integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl ˜ ( 4 ) is presented. As an application example, we construct a new integrable couplings of the Dirac soliton hierarchy with self-consistent sources by using of loop algebra sl ˜ ( 4 ) .

A nonlinear integrable couplings of C-KdV soliton hierarchy and its infinite conservation laws

Abstract A kind of nonlinear integrable couplings of C-KdV soliton hierarchy is constructed, then we present the infinitely many conservation laws for the nonlinear integrable couplings of the C-KdV soliton hierarchy.

Continuous limits for an integrable coupling of the Kac-Van Moerbeke hierarchy

In this paper, we present an integrable coupling of lattice hierarchy and its continuous limits by using Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling of Kac-Van Moerbeke lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable coupling of discrete soliton equation hierarchy, which has the integrable coupling system of MKdV hierarchy as a new kind of continuous limit.

Three-dimensional exact solutions of Gross-Pitaevskii equation with variable coefficients

A three-dimensional Gross-Pitaevskii (3D-GP) equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrodinger (NLS) equation. We study exact solutions of the 3D-GP equation with (space, time)-modulated potential and nonlinearity. In particular, based on the similarity transformation, we report several families of exact solutions of the 3D-GP equation with different amplitude surfaces, in which some physically relevant solutions are described. These results may raise the possibility of relative experiments and potential applications.

The generalized Kupershmidt deformation for the fifth-order coupled KdV equations hierarchy

Abstract Based on the Kupershmidt deformation, we propose the generalized Kupershmidt deformation (GKD) to construct new systems from integrable bi-Hamiltonian system. As applications, the generalized Kupershmidt deformation of the fifth-order coupled KdV equations hierarchy with self-consistent sources and its Lax representation are presented.

Noncommutative integrable coupling system of TC equation hierarchy

A noncommutative version of the TC soliton equation hierarchy is presented, which possesses the zero curvature representation. Then, we show that noncommutative (NC) TC equation can be derived from the noncommutative (anti-)self-dual Yang-Mills equation by reduction. Finally, an integrable coupling system of the NC TC equation hierarchy is constructed by using of the enlarged Lax pairs.

Constructing (2+1)-dimensional nonlinear soliton equations with a generalized zero curvature equation

The generalized zero curvature equation is presented, which is an important tool to construct the (2+1)-dimensional integrable soliton equation hierarchy. A few of new (2+1)-dimensional integrable soliton equation hierarchies are obtained through the generalized zero curvature equation.

A new integrable hierarchy and constrained flows, its expanding integrable system

Abstract A new subalgebra of loop algebra A ∼ 2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. Furthermore, by making use of bi-symmetry constraints, the generalized Hamiltonian regular representations for the hierarchy are obtained. Finally, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G ∼ .