The stability of degenerate solitons for derivative nonlinear Schrodinger equations

In this paper, we consider the following nonlinear Schr & ouml;dinger equation with derivative: i partial derivative(t)u + partial derivative(xx)u + i|u|(2)partial derivative(x)u + b|u|(4) u = 0, (t, x ) is an element of R x 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, IIu(t)IIL66 > root delta. In this paper, we remove this condition for the non -positive initial energy and momentum, and we extend the stability result for b >= 0. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.