Focusing revisited: a renormalization/bifurcation approach
Focusing revisited: a renormalization/bifurcation approach
复制标题
重新审视聚焦：重正化/分岔方法
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Kevrekidis
中科院分区：
文献类型：
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作者：
C. Siettos;I. Kevrekidis;P. Kevrekidis
非线性薛定谔（NLS）方程是保守色散系统的包络波方程的一个普遍存在的例子。我们在这里重新审视的问题，自相似聚焦的波的情况下，通过棱镜的基于模板的动态重整化技术，因子的自相似性，并产生一个分叉的观点开始聚焦的NLS方程的聚焦。因此，识别聚焦自相似解成为稳态问题。随后获得的稳定状态和它们的线性稳定性进行了数值研究。计算是在可变折射率的设置中进行的，其中，聚焦的开始出现作为一种新型的混合哈密顿耗散动力系统的超临界分岔（在某种程度上，让人想起干草叉分岔）。
The nonlinear Schrodinger (NLS) equation is a ubiquitous example of an envelope wave equation for conservative, dispersive systems. We revisit here the problem of self-similar focusing of waves in the case of the focusing NLS equation through the prism of a template-based dynamic renormalization technique that factors out self-similarity and yields a bifurcation view of the onset of focusing. As a result, identifying the focusing self-similar solution becomes a steady-state problem. The steady states are subsequently obtained and their linear stability is numerically examined. The calculations are performed in the setting of variable index of refraction, in which the onset of focusing appears as a supercritical bifurcation of a novel type of mixed Hamiltonian-dissipative dynamical system (reminiscent, to some extent, of a pitchfork bifurcation).