Global existence for the derivative nonlinearSchrödinger equation with arbitrary spectral singularities
Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem
Abstract
We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space [math] . Our result exploits the complete integrability of the DNLS equation and removes certain spectral conditions on the initial data required by our previous work, thanks to Zhou’s analysis (Comm. Pure Appl. Math. 42:7 (1989), 895–938) on spectral singularities in the context of inverse scattering.
Topics & Concepts
MathematicsGravitational singularitySobolev spaceContext (archaeology)Nonlinear systemMathematical analysisDerivative (finance)InverseSpace (punctuation)Inverse problemSpectral theorySpectrum (functional analysis)Spectral analysisSpectral methodSpectral propertiesDomain (mathematical analysis)Time derivativeSpectral functionPure mathematicsDispersive partial differential equationInverse scattering problemSingularitySpectral spaceAdvanced Mathematical Physics ProblemsNonlinear Waves and SolitonsNonlinear Photonic Systems