论文标题
在分数非线性schroedinger方程中单峰孤子的稳定，具有诱捕电势
Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential
论文作者
论文摘要
我们以分数非线性Schroedinger方程（FNSE）的框架中局部模式的存在和稳定性，并通过聚焦的立方或聚焦的立方质量非线性以及狭窄的谐波启动器（HO）电位。以Hermite-Gauss模式的形式获得了近似分析溶液。线性稳定性分析和直接模拟表明，在立方体自我关注的作用下，单峰基态和偶极模式在征费指数（分级性度）alpha = 1和alpha <1的值时稳定在ho电位上，这分别导致了自由空间中的关键或超紧密崩溃。除此之外，五五重量自我排列的包含提供了高阶模式的稳定，至少，局部峰的数量至少为七个。
We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal that, under the action of the cubic self-focusing, the single-peak ground state and dipole mode are stabilized by the HO potential at values of the Levy index (the fractionality degree) alpha = 1 and alpha < 1, which lead, respectively, to the critical or supercritical collapse in free space. In addition to that, the inclusion of the quintic self-defocusing provides stabilization of higher-order modes, with the number of local peaks up to seven, at least.
