ORIGINAL PAPERS

Action-Angle Variables for the Lie-Poisson Hamiltonian Systems Associated with the Manakov Equation

  • Xue Geng ,
  • Liang Guan
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  • Anyang Normal University, Anyang, 455000, Henan, China

Received date: 2024-09-11

  Revised date: 2024-09-11

  Online published: 2026-04-07

Supported by

This work was supported by the National Natural Science Foundation of China (No. 12001013).

Abstract

In this study, we introduce two finite-dimensional Lie-Poisson Hamiltonian systems related to the Manakov equation through the nonlinearization method. Additionally, we apply the separation of variables on the common level set of Casimir functions to analyze these systems, which are related to the non-hyperelliptic algebraic curve. Ultimately, we construct the action-angle variables for these systems based on the Hamilton-Jacobi theory and derive the Jacobi inversion problem for the Manakov equation.

Cite this article

Xue Geng , Liang Guan . Action-Angle Variables for the Lie-Poisson Hamiltonian Systems Associated with the Manakov Equation[J]. Communications on Applied Mathematics and Computation, 2026 , 8(2) : 705 -721 . DOI: 10.1007/s42967-024-00465-z

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