Stability of the traveling waves for the derivative Schr\"odinger equation in the energy space
Abstract
In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schr\"odinger 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 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 ColinOhta-DNLS, where Colin and Ohta made use of the concentration-compactness argument.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.