Stability of multiple-pulse solutions
Stability of multiple-pulse solutions
复制标题
多脉冲解的稳定性
DOI：
10.1090/s0002-9947-98-01673-0
复制
发表时间：
1998
影响因子：
1.3
通讯作者：
Bjorn Sandstede
中科院分区：
文献类型：
--
作者：
Bjorn Sandstede
研究了半线性抛物型方程多脉冲解在真实的直线上的稳定性。本文导出了一个确定从一个稳定的主脉冲分叉出的N个脉冲的稳定性的方程组。该系统仅依赖于导致N脉冲存在的特定分岔。作为例子，研究了当主脉冲收敛于鞍焦点时多脉冲的存在性和稳定性。结果表明，在适当的假设下，对于任何固定的N > 1，无穷多个N脉冲分叉。其中有无数稳定的。事实上，在右半平面中，可以指定0到N-1之间的任何数目的特征值。
In this article, stability of multiple-pulse solutions in semilinear parabolic equations on the real line is studied. A system of equations is derived which determines stability of N-pulses bifurcating from a stable primary pulse. The system depends only on the particular bifurcation leading to the existence of the N-pulses. As an example, existence and stability of multiple pulses are investigated if the primary pulse converges to a saddle-focus. It turns out that under suitable assumptions infinitely many N-pulses bifurcate for any fixed N > 1. Among them are infinitely many stable ones. In fact, any number of eigenvalues between 0 and N − 1 in the right half plane can be prescribed.