Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation
Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation
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DOI：
10.3389/fphy.2023.1285301
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发表时间：
2023-12
影响因子：
3.1
通讯作者：
Xue Geng;Dianlou Du;Xianguo Geng
中科院分区：
文献类型：
--
作者：
Xue Geng;Dianlou Du;Xianguo Geng
本文利用非线性化方法给出了两个与Hirota-Satsuma修正Boussinesq方程相关联的有限维Lie-Poisson Hamilton系统。此外，本文还引入Casimir函数公共水平集上的分离变量方法，研究了这类非超椭圆代数曲线系统。最后，根据Hamilton-Jacobi理论，构造了这些系统的作用角变量，得到了Hirota-Satsuma修正Boussinesq方程的Jacobi反演问题.
In this work, we present two finite-dimensional Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation by using the nonlinearization method. Moreover, the separation of variables on the common level set of Casimir functions is introduced to study these systems which are associated with a non-hyperelliptic algebraic curve. Finally, in light of the Hamilton–Jacobi theory, the action-angle variables for these systems are constructed, and the Jacobi inversion problem associated with the Hirota–Satsuma modified Boussinesq equation is obtained.