Roberts-Jones solitary waves on the two-dimensional sphere

Abstract: Roberts-Jones solitary waves, also known as Roberts-Jones solitons, are fully nonlinear, localised traveling wave solutions of the Gross-Pitaevskii equation in two and three spatial dimensions [1]. At low speeds, these waves manifest as vortex dipoles in two dimensions and vortex rings in three dimensions, creating topological excitations in the field’s phase. As the wave speed approaches a critical value, the vortex structure vanishes, leaving behind a simple dip in the field’s amplitude. In this work, we explore the existence and stability of Roberts-Jones solitary waves in curved spatial geometries, specifically on the two-dimensional sphere. We compare these solitonic structures with delocalised Bogoliubov excitations, shedding light on their role in novel experimental realisations of ultracold atomic gases confined within spherical shells. Our findings offer new insights into the interplay between geometry and nonlinear wave dynamics in quantum fluids.

Mathematicsfluid dynamics

Audience: researchers in the topic

Fluids and Structures Seminar @ UEA