The stability of degenerate solitons for derivative nonlinear Schrödinger equations

Abstract

In this paper, we consider the following nonlinear Schrödinger equation with derivative:i∂tu+∂xxu+i|u|2∂xu+b|u|4u=0,(t,x)∈R×R,b≥0. For the case b=0, the original DNLS, Kwon and Wu [14] proved the conditional orbital stability of degenerate solitons including scaling, phase rotation, and spatial translation with a non-smallness condition, ‖u(t)‖L66>δ. In this paper, we remove this condition for the non-positive initial energy and momentum, and we extend the stability result for b≥0.