English

Self-similar solutions to the derivative nonlinear Schr\"odinger equation

Analysis of PDEs 2018-11-16 v1

Abstract

A class of self-similar solutions to the derivative nonlinear Schr\"odinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

Keywords

Cite

@article{arxiv.1811.06141,
  title  = {Self-similar solutions to the derivative nonlinear Schr\"odinger equation},
  author = {Kazumasa Fujiwara and Vladimir Georgiev and Tohru Ozawa},
  journal= {arXiv preprint arXiv:1811.06141},
  year   = {2018}
}

Comments

16 pages, no figures