AUTHOR=Geng Xue , Du Dianlou , Geng Xianguo TITLE=Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation JOURNAL=Frontiers in Physics VOLUME=11 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1285301 DOI=10.3389/fphy.2023.1285301 ISSN=2296-424X ABSTRACT=

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.