English

Solutions with expanding compact support of saturated Schr{\"o}dinger equations: self-similar solutions

Analysis of PDEs 2025-06-06 v1

Abstract

We prove the existence of solutions u(t,x)u(t,x) of the Schr{\"o}dinger equation with a saturation nonlinear term (u/u)(u/|u|) having compact support, for each t>0,t>0, that expands with a growth law of the type CtC\sqrt{t}. The primary tool is considering the self-similar solution of the associated equation. For more information see https://ejde.math.txstate.edu/Volumes/2025/53/abstr.html

Keywords

Cite

@article{arxiv.2506.04691,
  title  = {Solutions with expanding compact support of saturated Schr{\"o}dinger equations: self-similar solutions},
  author = {Pascal Bégout and Jesus Ildefonso Diaz},
  journal= {arXiv preprint arXiv:2506.04691},
  year   = {2025}
}