非齐次散焦非线性非多项式薛定谔方程中的亮孤子
Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities
摘要：
本文在一维Muñoz-Mateo - Delgado（MM-D）方程的框架下，扩展了空间非均匀非线性模型的研究工作，研究了非多项式自散焦（SDF）非线性产生的亮孤子（具有SDF非线性的Gross-Pitaevskii方程的一维简化），其中非线性的局部强度在坐标x的大值处以比|x|更快的任何速率增长。我们产生的数值解和解析解，获得的手段，无节点的基态，和激发模式与1，2，3，和4个节点，在两个版本的模型，陡峭的（指数）和温和的（代数）非线性调制配置文件。在这两种情况下，基态和单节点模式是完全稳定的，而高阶模式的稳定性取决于它们的范数（在代数调制的情况下，它们是完全不稳定的）。不稳定状态自发地演化成稳定的低阶对应物。
英文摘要：
Extending the recent work on models with spatially nonuniform nonlinearities, we study bright solitons generated by the nonpolynomial self-defocusing (SDF) nonlinearity in the framework of the one-dimensional (1D) Muñoz-Mateo - Delgado (MM-D) equation (the 1D reduction of the Gross-Pitaevskii equation with the SDF nonlinearity), with the local strength of the nonlinearity growing at any rate faster than |x| at large values of coordinate x. We produce numerical solutions and analytical ones, obtained by means of the Thomas-Fermi approximation (TFA), for nodeless ground states, and for excited modes with 1, 2, 3, and 4 nodes, in two versions of the model, with the steep (exponential) and mild (algebraic) nonlinear-modulation profiles. In both cases, the ground states and the single-node ones are completely stable, while the stability of the higher-order modes depends on their norm (in the case of the algebraic modulation, they are fully unstable). Unstable states spontaneously evolve into their stable lower-order counterparts.
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