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.

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

References in corpus (4)

• Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation
• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
• Existence of global solutions to the derivative NLS equation with the inverse scattering transform method
• Solitary waves for nonlinear Schrödinger equation with derivative

Cited by in corpus (6)

• A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation
• Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case
• On the stability of periodic waves for the cubic derivative NLS and the quintic NLS
• Solitary waves for nonlinear Schrödinger equation with derivative
• Stability of the sum of two solitary waves for (gDNLS) in the energy space
• Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the endpoint case