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A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation.
- Source :
-
Theoretical & Mathematical Physics . Mar2024, Vol. 218 Issue 3, p370-387. 18p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HAMILTONIAN systems
*EQUATIONS
*HAMILTON-Jacobi equations
Subjects
Details
- Language :
- English
- ISSN :
- 00405779
- Volume :
- 218
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Theoretical & Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 176221324
- Full Text :
- https://doi.org/10.1134/S0040577924030024