@article{Geng2022, 
author = {Xue Geng and Liang Guan and Dianlou Du},
title = {Action-angle variables for the Lie-Poisson Hamiltonian systems associated with the three-wave resonant interaction system},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {9989-10008},
keywords = {three-wave resonant interaction system, non-hyperelliptic algebraic curve, separated variables, action-angle variables},
url = {https://www.sciopen.com/article/10.3934/math.2022557},
doi = {10.3934/math.2022557},
abstract = {The              g      l        3    (      C    ) rational Gaudin model governed by    3  ×  3 Lax matrix is applied to study the three-wave resonant interaction system (TWRI) under a constraint between the potentials and the eigenfunctions. And the TWRI system is decomposed so as to be two finite-dimensional Lie-Poisson Hamiltonian systems. Based on the generating functions of conserved integrals, it is shown that the two finite-dimensional Lie-Poisson Hamiltonian systems are completely integrable in the Liouville sense. The action-angle variables associated with non-hyperelliptic spectral curves are computed by Sklyanin's method of separation of variables, and the Jacobi inversion problems related to the resulting finite-dimensional integrable Lie-Poisson Hamiltonian systems and three-wave resonant interaction system are analyzed.}
}