Spontaneous symmetry and antisymmetry breaking of solitons in quintic nonlinearity

This paper presents a systematic investigation of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) processes for solitons governed by the one-dimensional nonlinear Schrödinger equation with pure quintic nonlinearity and a δ-function double-well potential. We analyze the evolution, stability, and power characteristics of solitons under both self-focusing (attractive) and self-defocusing (repulsive) nonlinearities. Through a combination of analytical methods and numerical simulations (including linear stability analysis and finite-difference time-domain method), we find the following: under self-defocusing nonlinearity, antisymmetric solitons undergo SASB as the propagation constant k increases, transforming into asymmetric solitons that are mostly unstable in the high-k region. Under self-focusing nonlinearity, symmetric solitons undergo SSB as k increases, yielding asymmetric solitons that remain stable for all values of k. While an increase of the nonlinearity strength reduces the soliton power, it leaves the symmetry-breaking threshold unaffected, highlighting its role in power scaling rather than in stability. The major novelty of our results lies in the qualitatively different stability behavior discovered in pure quintic nonlinear systems, as opposed to cubic or mixed cubic-quintic systems. Thus, our study reveals, for the first time, the distinct stability properties of SSB and SASB states in a quintic nonlinear system. Our findings advance the theoretical framework of soliton symmetry breaking under higher-order nonlinearity and provide key insights for designing nonlinear optical devices and controlling states in Bose–Einstein condensates.