Two-dimensional ring-like vortex and multisoliton nonlinear structures at the upper-hybrid resonance

TL;DR

This paper develops 2D equations for nonlinear wave interactions at the upper-hybrid resonance, demonstrating the existence and stability of various localized structures including solitons and vortices through numerical analysis.

Contribution

It introduces a new 2D nonlinear model with nonlocal effects and proves the absence of collapse, identifying stable localized wave structures.

Findings

Existence of stable 2D fundamental solitons with negative Hamiltonian

Numerical discovery of various localized structures like vortices and multisolitons

Proof of no collapse in the nonlinear model

Abstract

Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear structures. A rigorous proof of the absence of collapse in the model is given. We have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (two-hump solitons, dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that 2D fundamental solitons with negative hamiltonian are stable.