Planar and radial kinks in nonlinear Klein-Gordon models: Existence, stability, and dynamics
Planar and radial kinks in nonlinear Klein-Gordon models: Existence, stability, and dynamics
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非线性 Klein-Gordon 模型中的平面和径向扭结：存在性、稳定性和动力学
DOI：
10.1103/physreve.98.052217
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发表时间：
2018
影响因子：
2.4
通讯作者：
R. Carretero
中科院分区：
文献类型：
--
作者：
P. Kevrekidis;I. Danaila;J. Caputo;R. Carretero
我们有效地考虑了二维非线性Klein-Gordon模型中的一维平面和径向扭结，并重点研究了sine-Gordon模型及其变体。我们采用了最近发展的绝热不变公式的非线性薛定谔方程，我们研究了这些扭结的横向稳定性。这使我们能够将一维平面扭结表征为孤子细丝，其定态和相应的光谱稳定性不仅可以在均匀的情况下表征，而且可以在存在外部电势的情况下表征。除此之外，完整的非线性（横向）动态的这种细丝使用减少，一维，绝热不变的配方。对于径向扭结，这种方法证实了它们的方位稳定性。它还预测了产生静止和稳定的环状扭结的可能性。在所有情况下，我们都用原始sine-Gordon和$\phi^4 $模型的完整数值来证实我们的方法的结果。
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently developed for nonlinear Schr{\"o}dinger equations, and we study the transverse stability of these kinks. This enables us to characterize one-dimensional planar kinks as solitonic filaments, whose stationary states and corresponding spectral stability can be characterized not only in the homogeneous case, but also in the presence of external potentials. Beyond that, the full nonlinear (transverse) dynamics of such filaments are described using the reduced, one-dimensional, adiabatic invariant formulation. For radial kinks, this approach confirms their azimuthal stability. It also predicts the possibility of creating stationary and stable ring-like kinks. In all cases we corroborate the results of our methodology with full numerics on the original sine-Gordon and $\phi^4$ models.