A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
Vladimir Dragovi\'c, Borislav Gaji\'c, Bo\v{z}idar Jovanovi\'c
TL;DR
This paper demonstrates that the motion of a particle in a homogeneous magnetic field on spheres of any dimension is completely integrable, providing a Lax representation and explicit integrals.
Contribution
It introduces a Lax representation for these magnetic flows and proves their complete integrability in all dimensions, a novel generalization.
Findings
Lax representation for magnetic flows on spheres
Complete integrability in all dimensions
Explicit first integrals of degree one and two
Abstract
We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere . We provide a Lax representation of the equations of motion and prove complete integrability of those systems for any . The integrability is provided via first integrals of degree one and two.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Partial Differential Equations · Advanced Differential Equations and Dynamical Systems