论文标题
谐振非线性schrödinger方程中的孤立波：稳定性和动力学特性
Solitary waves in the resonant nonlinear Schrödinger equation: stability and dynamical properties
论文作者
论文摘要
考虑了所谓的共振非线性schrödinger（RNLS）方程的稳定性和动力学特性。 RNLS是非线性schrödinger（NLS）方程的变体，并添加用于描述无碰撞等离子体中波传播的扰动。我们首先检查了RNLS模型中平面波的模量稳定性，从而确定了NLS情况相关条件的修改。然后，我们转到对具有消失和非零边界条件的孤立波的研究。有趣的是，RNL与通常的NLS一样，根据分散和非线性的相对迹象表现出深色和明亮的孤子解决方案。在这项工作中，系统地研究了这些解决方案的相应存在，稳定性和动力学。
The stability and dynamical properties of the so-called resonant nonlinear Schrödinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrödinger (NLS) equation with the addition of a perturbation used to describe wave propagation in cold collisionless plasmas. We first examine the modulational stability of plane waves in the RNLS model, identifying the modifications of the associated conditions from the NLS case. We then move to the study of solitary waves with vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright soliton solutions depending on the relative signs of dispersion and nonlinearity. The corresponding existence, stability and dynamics of these solutions are studied systematically in this work.
