Orbital stability of solitary waves for derivative nonlinear Schrödinger equation

Abstract

In this paper, we show the orbital stability of solitons arising in the cubic derivative nonlinear Schrodinger equations. We consider the zero mass case that is not covered by earlier works [8, 3]. As this case enjoys L^2 scaling invariance, we expect the orbital stability in the sense up to scaling symmetry, in addition to spatial and phase translations. For the proof, we are based on the variational argument and extend a similar argument in [21]. Moreover, we also show a self-similar type blow up criteria of solutions with the critical mass 4π.

Error is fixed and Theorem 1 is changed

References in corpus (1)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data

Cited by in corpus (7)

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• Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case
• Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the endpoint case
• The derivative NLS equation: global existence with solitons
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative
• Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in $H^{\frac{1}{2}}$