A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions

2025/06/29 by Vladimir Dragović, Dragović, Vladimir, Borislav Gajić +3 · 1 citation
Mathematics · #37J35 #53D25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.23299

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere S^n-1. We provide a Lax representation of the equations of motion for arbitrary n and prove integrability of those systems in the Liouville sense. The integrability is provided via first integrals of degree one and two.

Citations

• Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
• Integrability of homogeneous exact magnetic flows on spheres
• Non-commutative Integrability, Moment Map and Geodesic Flows

Cited by

• Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
• Contact magnetic geodesic and sub-Riemannian flows on V_n,2 and integrable cases of a heavy rigid body with a gyrostat

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• Integrability of homogeneous exact magnetic flows on spheres
• Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
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• Contact magnetic geodesic and sub-Riemannian flows on V_n,2 and integrable cases of a heavy rigid body with a gyrostat