A hierarchy of integrable nonlinear lattice equations and its two integrable coupling systems文档.pdf

Applied Mathematics and Computation 203 (2008) 7–13 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: /locate/amc A hierarchy of integrable nonlinear lattice equations and its two integrable coupling systems Lin-Lin Ma *, Xi-Xiang Xu College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China a r t i c l e i n f o a b s t r a c t Keywords: Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations Spectral problem is derived. It is shown that the hierarchy is integrable in the Liouville sense. A few subal- Integrable coupling gebras of the Lie algebra are constructed from which the corresponding loop algebras can Lax pair be presented. It follows that the enlarging algebra systems are introduced. Moreover, we Discrete integrable equation construct the two integrable coupling systems with the help of the enlarging algebra Enlarging algebra systems systems. Crown Copyright 2008 Published by Elsevier Inc. All rights reserved. 1. Introduction In recent 20 years, the search for discrete integrable systems has been given a novel impetus [1–10]. Many integrable nonlinear integrable lattice equations have been studied systematically, such as the Ablowitz Lodik lattice, the Toda lattice, the discrete KdV equation, and so on [1–11]. Searching for new integrable lattice equations, in lattice soliton theory, is