New Positive and Negative Hierarchies of Integrable Differential-Difference Equations and Conservation Laws

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2009,（1）
• 页码范围: 17-22
• 页数: 6页
• 语种: 英文

摘要

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rationed type. Further, we construct infinite conservation laws about the positive hierarchy.