论文标题
分数维度中空间kerr孤子的对称破坏
Symmetry breaking of spatial Kerr solitons in fractional dimension
论文作者
论文摘要
我们研究了孤子子在非线性分数Schrödinger方程（NLFSE）框架中的对称性破坏，其特征在于其Lévy指数，具有立方非线性和对称的双层电势。发现了不对称，对称和反对称孤子溶液，通过稳定的不对称孤子溶液从不稳定的对称和抗对称的溶液中通过对称性分叉形成。两种不同的分叉场景是可能的。首先，对称的孤子溶液在自我焦点的非线性的作用下，对干草叉类型的对称性分叉进行了对称性分叉，从而产生了不对称孤子的分支。其次，在自我消灭非线性的情况下，通过倒置式fit型类型的类型自我排列的非对称状态分支。系统的数值分析表明，列维指数的增加会导致对称区域的收缩或扩展，具体取决于双孔电位的参数。根据Lévy指数的变化，探索了孤子溶液的稳定性，并通过直接数值模拟确认结果。
We study symmetry breaking of solitons in the framework of a nonlinear fractional Schrödinger equation (NLFSE), characterized by its Lévy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric, and antisymmetric soliton solutions are found, with stable asymmetric soliton solutions emerging from unstable symmetric and antisymmetric ones by way of symmetry-breaking bifurcations. Two different bifurcation scenarios are possible. First, symmetric soliton solutions undergo a symmetry-breaking bifurcation of the pitchfork type, which gives rise to a branch of asymmetric solitons, under the action of the self-focusing nonlinearity. Second, a family of asymmetric solutions branches off from antisymmetric states in the case of self-defocusing nonlinearity through a bifurcation of an inverted-pitchfork type. Systematic numerical analysis demonstrates that increase of the Lévy index leads to shrinkage or expansion of the symmetry-breaking region, depending on parameters of the double-well potential. Stability of the soliton solutions is explored following the variation of the Lévy index, and the results are confirmed by direct numerical simulations.
