Orbital stability of solitary waves for derivative nonlinear Schr\"odinger 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 4{\pi}.