English

Modified Scattering and Asymptotic Completeness for the Derivative Nonlinear Schr\"odinger equation

Analysis of PDEs 2025-08-26 v1

Abstract

We prove a modified scattering and asymptotic completeness for the derivative nonlinear Schr\"odinger equation. This is the first result proving asymptotic completeness in a quasilinear setting. Our approach combines the method of testing by wave packets, introduced by Ifrim and Tataru, a bootstrap argument, and the Klainerman Sobolev vector field method.

Keywords

Cite

@article{arxiv.2508.16794,
  title  = {Modified Scattering and Asymptotic Completeness for the Derivative Nonlinear Schr\"odinger equation},
  author = {Allison Byars},
  journal= {arXiv preprint arXiv:2508.16794},
  year   = {2025}
}