Finite-genus solutions for the Ablowitz-Ladik hierarchy
Finite-genus solutions for the Ablowitz-Ladik hierarchy
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DOI：
10.1088/0305-4470/32/26/316
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发表时间：
1999-03
期刊：
影响因子：
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通讯作者：
V. Vekslerchik
中科院分区：
文献类型：
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作者：
V. Vekslerchik
通过建立Ablowitz-Ladik族（ALH）与-函数的Fay恒等式之间的关系，研究了构造ALH的有限亏格拟周期解的问题.它表明，使用一个限制程序，可以从后者推导出无穷多个微分恒等式，它可以被安排为一个无限的微分差分方程组与ALH的方程相吻合，原来的费伊的身份可以被改写的形式类似的功能方程代表ALH已在以前的作品中推导出的作者。这提供了一种算法，获得一些类的拟周期解的ALH，这可以被看作是一种替代的逆散射变换或代数几何方法。
The question of constructing the finite-genus quasiperiodic solutions for the Ablowitz-Ladik hierarchy (ALH) is considered by establishing relations between the ALH and Fay's identity for the -functions. It is shown that using a limiting procedure one can derive from the latter an infinite number of differential identities, which can be arranged as an infinite set of differential-difference equations coinciding with the equations of the ALH, and that the original Fay's identity can be rewritten in a form similar to the functional equations representing the ALH which have been derived in the previous works of the author. This provides an algorithm for obtaining some class of quasiperiodic solutions for the ALH, which can be viewed as an alternative to the inverse scattering transform or the algebro-geometrical approach.