Spontaneous symmetry breaking induced by nonlinear interaction in a coupler supported by fractional diffraction

TL;DR

This paper models coupled fractional nonlinear Schrödinger equations with a double-well potential, revealing how nonlinear interactions induce spontaneous symmetry breaking and affect soliton stability and localization.

Contribution

It introduces a novel fractional coupled Schrödinger model with a double-well potential and analyzes symmetry breaking and soliton stability within this framework.

Findings

Fractional diffraction influences soliton amplitude and localization.

Critical Lévy index values determine the formation of coupled ground state solitons.

Unstable asymmetric solitons exhibit oscillatory dynamics.

Abstract

In this paper we introduce a one-dimensional model of coupled fractional nonlinear Schr\"odinger equations with a double-well potential applied to one component. This study examines ground state (GS) solitons, observing spontaneous symmetry breaking (SSB) in both the actuated field and the partner component due to linear coupling. Numerical simulations reveal symmetric and asymmetric profiles arising from a slightly asymmetric initial condition. Asymmetry is influenced by nonlinearities, potential depth, and coupling strength, with self-focusing systems favoring greater asymmetry. Fractional diffraction affects the amplitude and localization of symmetric profiles and the stability of asymmetric ones. We identify critical L\'evy index values for generating coupled GS solitons. Stability analysis of unstable, centrally asymmetric GS solitons demonstrates oscillatory dynamics, providing new insights into SSB in fractional systems and half-trapped solitons.