Work

Integrability of certain Hamiltonian systems in 2D variable curvature spaces

Year: 2025

Type: article

Abstract: The objective of this work is to examine the integrability of Hamiltonian systems in 2D spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability. They are given in terms of arithmetic restrictions on values of the parameters describing the system. We apply the obtained results to some examples to illustrate that the applicability of the obtained result is easy and effective. Certain new integrable examples are given. The findings highlight the applicability of the differential Galois approach in studying the integrability of Hamiltonian systems in curved spaces, expanding our understanding of nonlinear dynamics and its potential applications.

Source: Europhysics Letters (EPL)

DOI: 10.1209/0295-5075/adc150

Authors: W. Szumiński, A. A. Elmandouh

Institutions: University of Zielona Góra, Mansoura University, King Faisal University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Narodowe Centrum Nauki

Award: G1794378920