Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation - Geng, Xue; Du, Dianlou; Geng, Xianguo (Frontiers in Physics, 2023)
In this work, we present two finite-dimensional Lie-Poisson Hamiltonian systems associated with the Hirota-Satsuma modified Boussinesq equation by using the nonlinearization methord.Moreover, the separation of variables on the common level set of Casimir functions are introduced to study these systems which are associated with non-hyperelliptic algebraic curve. Finally, in the light of 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.