Discrete Soliton Hierarchy Research Articles

Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs

The Darboux transformation method with 4×4 spectral problem has more complexity than 2×2 and 3×3 spectral problems. In this paper, we start from a new discrete spectral problem with a 4×4 Lax pairs and construct a lattice hierarchy by properly choosing an auxiliary spectral problem, which can be reduced to a new discrete soliton hierarchy. For the obtained lattice integrable coupling equation, we establish a Darboux transformation and apply the gauge transformation to a specific equation and then the explicit solutions of the lattice integrable coupling equation are obtained. Copyright © 2017 John Wiley & Sons, Ltd.

A New 3×3 Discrete Soliton Hierarchy with Self-Consistent Sources

In this paper, we consider a discrete soliton hierarchy with self-consistent sources by using higher-dimensional matrix spectral problem. Then a new discrete soliton hierarchy with self-consistent sources is obtained.

A Higher-Dimensional Lie Algebra and 4×4 Discrete Soliton Hierarchy with Self-Consistent Sources

In this paper, we aim to construct a super integrable discrete soliton hierarchy with self-consistent sources. A new isospectral problem is firstly presented, and we consider a discrete soliton hierarchy with self-consistent sources by using Lie algebra . Then, a new higher dimensional super integrable discrete soliton hierarchy with self-consistent sources is obtained. The method can be generalized to other soliton hierarchy with self-consistent sources.

A nonlinear discrete integrable coupling system and its infinite conservation laws

We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy. As an explicit application of the method proposed in the paper, the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.

New form (2 + 1)-dimensional integrable lattice hierarchies with two shift operators [formula omitted] and [formula omitted

We present a new method to construct two (2+1)-dimensional lattice hierarchies. By considering a kind of spectral problems with two shift operators E˜ and Eˆ, a new (2+1)-dimensional discrete soliton hierarchy and a new 3×3 lattice hierarchy are constructed by using 3×3 matrix spectral problem.

Infinite Conservation Laws for Nonlinear Integrable Couplings of Toda Hierarchy

We construct nonlinear integrable couplings of discrete soliton hierarchy, then the infinite conservation laws for the nonlinear integrable couplings of the lattice hierarchy are established. For explicit application of the method proposed, the infinite conservation laws of nonlinear integrable couplings of the Toda lattice hierarchy are presented. The obtained integrable couplings of the Toda lattice equations and conservation laws can be used to describe the possible formation mechanisms for hydrodynamics, solid state physics and plasma physics, respectively.

A BLASZAK–MARCINIAK LATTICE HIERARCHY WITH SELF-CONSISTENT SOURCES

In this paper, we consider the discrete soliton hierarchy with self-consistent sources by using Lie algebra sl(3). Then a Blaszak–Marciniak equations hierarchy with self-consistent sources is obtained through the discrete zero curvature equation.

Algebro-geometric solutions for some [formula omitted]-dimensional discrete systems

Starting from a discrete spectral problem, a discrete soliton hierarchy is derived. Some ( 2 + 1 ) -dimensional discrete systems related to the hierarchy are proposed. The elliptic coordinates are introduced and the equations in the discrete soliton hierarchy are decomposed into solvable ordinary differential equations. The straightening out of the continuous flow and the discrete flow are exactly given through the Abel–Jacobi coordinates. As an application, explicit algebro-geometric solutions for the ( 2 + 1 ) -dimensional discrete systems are obtained.