可积系统
数学
等级制度
松驰对
标量(数学)
拉格朗日
纯数学
班级(哲学)
非线性系统
域代数上的
数学物理
数学分析
几何学
物理
量子力学
计算机科学
人工智能
经济
市场经济
作者
Duncan Sleigh,F.W. Nijhoff,Vincent Caudrelier
标识
DOI:10.1016/j.geomphys.2019.03.015
摘要
It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure. We show that, as a consequence of this multiform structure, we can formulate a variational principle for the Lax pair itself, a problem that to our knowledge was never previously considered. As an example, we present an integrable $N\times N$ matrix system that contains the AKNS hierarchy, and we exhibit the Lagrangian multiform structure of the scalar AKNS hierarchy by presenting the components corresponding to the first three flows of the hierarchy.
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