Geodesic
A~nonlocal finite-dimensional integrable system related to the
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 430-448

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We propose a hierarchy of the nonlocal mKdV (NmKdV) equation. Based on a constraint, we obtain nonlocal finite-dimensional integrable systems in a Lie–Poisson structure. By a coordinate transformation, the nonlocal Lie–Poisson Hamiltonian systems are reduced to nonlocal canonical Hamiltonian systems in the standard symplectic structure. Moreover, using the nonlocal finite-dimensional integrable systems, we give parametric solutions of the NmKdV equation and the generalized nonlocal nonlinear Schrödinger (NNLS) equation. According to the Hamilton–Jacobi theory, we obtain the action–angle-type coordinates and the inversion problems related to Lie–Poisson Hamiltonian systems.
Keywords: nonlocal integrable system, Lie–Poisson Hamiltonian system
Mots-clés : nonlocal mKdV equation, action–angle type variables. 
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Xue Wang; Dianlou Du; H. Wang. A~nonlocal finite-dimensional integrable system related to the. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 430-448. http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a1/