论文标题
分数非线性schrödinger方程中的涡旋孤子，具有立方骨折的非线性
Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
论文作者
论文摘要
我们解决了具有竞争性的立方Quintic非线性的分数非线性schrödinger方程（NLSE）的涡流溶液（VS）溶液的存在和稳定性，并以1 \leqα\ leq2为单位。具有涡度S = 1,2的环形VSS家族，以数值形式构建3个。与通常的二维NLSE（对应于α= 2）不同，在分数模型VSS中存在于总功率的有限阈值之上，p。研究了VS溶液的稳定性，以线性化方程为控制，并通过直接模拟证实。不稳定的VSS通过方位角扰动分解为几个片段，它们的数量取决于小扰动的最快生长本本特征。根据P的定义，稳定性区域随着α的增加，在所有s = 1、2和3的α上增加到2，除了在1 \leqα\ leq1.3的间隔内s = 2的陡峭收缩。
We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schrödinger equation (NLSE) with competing cubic-quintic nonlinearities and the Lévy index (fractionality) taking values 1 \leqα\leq2. Families of ring-shaped VSs with vorticities s = 1,2, and 3 are constructed in a numerical form. Unlike the usual two-dimensional NLSE (which corresponds to α = 2), in the fractional model VSs exist above a finite threshold value of the total power,P. Stability of the VS solutions is investigated for small perturbations governed by the linearized equation, and corroborated by direct simulations. Unstable VSs are broken up by azimuthal perturbations into several fragments, whose number is determined by the fastest growing eigenmode of small perturbations. The stability region, defined in terms of P, expands with the increase of α from 1 up to 2 for all s = 1, 2, and 3, except for steep shrinkage for s = 2 in the interval of 1\leqα\leq1.3.
