Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities,Annalen Der Physik

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Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities
Annalen Der Physik ( IF 2.2 ) Pub Date : 2020-07-19 , DOI: 10.1002/andp.202000048
Pengfei Li ₁ , Chaoqing Dai ₂

Affiliation

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic‐quintic nonlinearity. Some prototypical characteristics of the symmetry breaking, featured by transformations of symmetric and antisymmetric soliton families into asymmetric ones, are found. Stable asymmetric solitons emerge from unstable symmetric and antisymmetric ones by way of two different symmetry breaking scenarios. A twisting branch, featured with double loops bifurcation, bifurcates off from the base branch of symmetric soliton solutions and crosses it, then merges into the base branch driven by the competitive nonlinear effect. A supercritical pitchfork bifurcation is bifurcated from the branch of antisymmetric soliton solutions and gives rise to a supercritical pitchfork bifurcation. Stability of the soliton families is explored by linear stability analysis. With the increase of the Lévy index, stability region induced by the twisting loops bifurcation is expanded. However, stability region of the pitchfork bifurcation is shrunk on the parameter plane of the Lévy index and the soliton power.

中文翻译：

具竞争三次三次非线性的分数阶非线性Schrödinger方程中光孤子的双环和Pitchfork对称打破分叉

在具有分数阶三次五阶非线性的非线性分数阶薛定ding方程（NLFSE）的框架下研究了孤子的对称打破分支。发现了对称破坏的一些典型特征，其特征是将对称和反对称孤子族转变为非对称族。稳定的非对称孤子通过两种不同的对称破坏情形从不稳定的对称和反对称孤子中出现。具有双环分支的扭曲分支从对称孤子解的基础分支分支并交叉，然后在竞争性非线性效应的驱动下合并为基础分支。超临界干草叉分叉从反对称孤子解的分支中分叉，产生超临界干草叉分叉。通过线性稳定性分析探索孤子族的稳定性。随着Lévy指数的增加，扭转环分叉引起的稳定区域扩大。但是，在Lévy指数和孤子功率的参数平面上，干草叉分叉的稳定区域缩小了。

更新日期：2020-07-19

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