Multipole solitons in competing nonlinear media with an annular potential

TL;DR

This paper explores the formation, stability, and dynamics of complex multipole solitons in nonlinear media with an annular potential, revealing their stability properties and rotational behavior through analytical and numerical analysis.

Contribution

It introduces the existence and stability analysis of multipole solitons in cubic-quintic media with an annular potential, including their rotation under phase torque.

Findings

Multiple soliton structures including dipole, quadrupole, and octupole are formed.

Stability domains persist even for multipole patterns with over 16 lobes.

Stable rotation of soliton complexes is demonstrated via phase torque application.

Abstract

We address the existence, stability, and propagation dynamics of multipole-mode solitons in cubic-quintic nonlinear media with an imprinted annular (ring-shaped) potential. The interplay of the competing nonlinearity with the potential enables the formation of a variety of solitons with complex structures, from dipole, quadrupole, and octupole solitons to necklace complexes. The system maintains two branches of soliton families with opposite slopes of the power-vs.-propagation-constant curves. While the solitons' stability domain slowly shrinks with the increase of even number $n$ of lobes in the multipole patterns, it remains conspicuous even for $n>16$. The application of a phase torque gives rise to stable rotation of the soliton complexes, as demonstrated by means of analytical and numerical methods.