کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4610362 | 1338558 | 2014 | 72 صفحه PDF | دانلود رایگان |
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein–Gordon equation utt−uxx+V′(u)=0utt−uxx+V′(u)=0, where u is a scalar-valued function of x and t , and the potential V(u)V(u) is of class C2C2 and periodic. Stability is considered both from the point of view of spectral analysis of the linearized problem (spectral stability analysis) and from the point of view of wave modulation theory (the strongly nonlinear theory due to Whitham as well as the weakly nonlinear theory of wave packets). The aim is to develop and present new spectral stability results for periodic traveling waves, and to make a solid connection between these results and predictions of the (formal) modulation theory, which has been developed by others but which we review for completeness.
Journal: Journal of Differential Equations - Volume 257, Issue 12, 15 December 2014, Pages 4632–4703