一族可积晶格方程及其守恒律

A Hierarchy of Integrable Lattice Equations and Corresponding Conservation Laws

文章旨在证明晶格方程族的Lax可积性以及求解方程族首个方程的一组无穷多守恒律。提出一个空间矩阵谱问题,通过计算求得一个与之相对应的时间矩阵谱问题,由空间谱问题和时间谱问题经过计算得到一族晶格方程,运用离散零曲率表示法,证明了该晶格方程族是Lax意义上可积的,运用谱矩阵的Lax对法求得了该晶格方程族首个方程的一组无穷多守恒律。

The paper is to verify the Lax integrability of lattice equations and solve infinitely many conservation laws of the first equation in the hierarchy of equations. A spatial matrix spectral problem is proposed, and a temporal matrix spectral problem is obtained through computing. A hierarchy of lattice equations are obtained through computing by the spatial spectral problem and temporal spectral problem, the Lax integrability for the lattice equations is proved through expression of discrete zero curvature,and infinitely many conservation laws of the first equation in the hierarchy of lattice equations are obtained by the way of Lax pairs of spectral matrix.