Stability of the traveling waves for the derivative Schrödinger equation in the energy space
Abstract
In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schrödinger equation with derivative (DNLS) in the energy space. Under some technical assumptions on the speed of each traveling wave, the stability of the sum of two traveling waves for DNLS is obtained in the energy space by Martel-Merle-Tsai's analytic approach in \cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS}. As a by-product, we also give an alternative proof of the stability of the single traveling wave in the energy space in \cite{ColinOhta-DNLS}, where Colin and Ohta made use of the concentration-compactness argument.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2017
- DOI:
- arXiv:
- arXiv:1702.07856
- Bibcode:
- 2017arXiv170207856M
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 49 pages, Te appear in Calculus of Variations and Partial Differential Equations. A few months after we submitted our paper, Le Coz and Wu obtained the stability of a k-soliton solution of (DNLS) independently