具有Liouville可积的非线性微分-差分方程族及其守恒律

A Liouville Integrable Nonlinear Differential-Difference Equation and its Conservation Laws

通过离散的零曲率表示导出了一个基于离散的矩阵谱问题的典型晶格孤子方程,同时证明了相应的晶格系统是Liouville可积的,进一步通过一个直接的办法给出了相应晶格系统的无穷多守恒律。

A lattice soliton equation is proposed as a typical lattice system in the hierarchy of lattice soliton equations by discrete zero curvature representation, which is derived from a discrete matrix spectral problem. The Liouville integrability for the corresponding lattice system is demonstrated. Moreover, infinitely many conservation laws of corresponding lattice system are obtained by a direct way.