Finite dimensional Hamiltonian systems and the algebro-geometry solution of the nonlocal reverse space–time sine-Gordon equation

Liang Guan, Xianguo Geng, Dianlou Du and Xue Geng

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: In this paper, we investigate the algebro-geometric solution of the novel integrable nonlocal reverse space–time sine-Gordon equation through the framework of nonlocal finite-dimensional Lie-Poisson Hamiltonian systems, which are generated by the nonlinearization method. The nonlocal reverse space–time sine-Gordon equation is introduced via the Lenard recursion equations. Under suitable constraints, this equation is nonlinearized into two nonlocal finite-dimensional Lie-Poisson Hamiltonian systems. By applying the separated variables, the nonlocal finite-dimensional Lie-Poisson Hamiltonian systems are reformulated as the canonical Hamiltonian systems with the standard symplectic structures. Furthermore, the relationship between the action–angle coordinates and the Jacobi inversion problem is established based on the Hamilton–Jacobi theory. In the end, the algebraic-geometric solution of the nonlocal reverse space–time sine-Gordon equation is obtained using the Riemann-Jacobi inversion.

Keywords: Nonlocal reverse space–time sine-Gordon equation; Lie-Poisson Hamiltonian systems; Jacobi inversion problem; Algebro-geometric solution (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013687

DOI: 10.1016/j.chaos.2024.115816

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