Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:414

Article

Chirilus-Bruckner, Martina¹  Duell, Wolf-Patrick²  Schneider, Guido² 

[1] Brown Univ, Providence, RI 02912 USA

[2] Univ Stuttgart, IADM, D-70569 Stuttgart, Germany

关键词: Modulation equation;    KdV equation;    NLS equation;    Approximation;   

DOI  :  10.1016/j.jmaa.2013.12.061

来源: Elsevier

【 摘 要 】

Bethuel et al. [1,2] and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of [1-3]. Our error estimates are based on a suitable choice of polar coordinates, a Cauchy-Kowalevskaya-like method, and energy estimates. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free