Orbital stability of solitary waves for derivative nonlinear Schrodinger 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. As this case enjoys L (2) scaling invariance, we expect orbital stability (up to scaling symmetry) in addition to spatial and phase translations. We also show a self-similar type blow up criterion of solutions with the critical mass 4 pi.