Dynamics of charges and solitons

Abstract

We first show that trajectories traced by charges moving in rotational magnetic fields are are, basically, the non-parallel geodesics of surfaces of revolution with coincident axis. Thus, people living in a surface of revolution are not able to sense the magnetic Hall e↵ect induced by the surrounding magnetic field and perceive charges as influenced, exclusively, by the gravity action on the surface of revolution. Secondly, the extended Hasimoto transformations are introduced and then used to identify trajectories of charges moving through a Killing rotational magnetic fields in terms of non-circular elastic curves. As a consequence, we see that in this case charges evolve along trajectories which are obtained as extended Hasimoto transforms of solitons of the filament equation.