广义非线性薛定谔方程中孤立波鞍结分岔处不存在稳定性切换。
No stability switching at saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations.
作者信息
Yang Jianke
机构信息
Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.
出版信息
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Mar;85(3 Pt 2):037602. doi: 10.1103/PhysRevE.85.037602. Epub 2012 Mar 30.
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that stability of solitary waves does not switch at saddle-node bifurcations. This analytical result is confirmed by numerical examples where both soliton branches are stable at saddle-node bifurcations.
鞍结分岔在各种物理系统的孤立波中频繁出现。以前人们认为，孤立波总是像在有限维动力系统中那样，在鞍结分岔处经历稳定性切换。在这里我们表明情况并非如此。对于一大类具有实势或复势的广义非线性薛定谔方程，我们证明孤立波的稳定性在鞍结分岔处不会切换。这一分析结果通过数值例子得到了证实，在这些例子中，两个孤子分支在鞍结分岔处都是稳定的。
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