Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term
Analysis of PDEs
2018-04-11 v2
Abstract
We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a mathematical model for the photonic crystal fiber oscillator. Regarding the ill-posedness, we show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map under slightly different conditions, respectively. We also prove the local unique existence of solutions in the analytic function space.
Keywords
Cite
@article{arxiv.1706.09111,
title = {Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term},
author = {Nobu Kishimoto and Yoshio Tsutsumi},
journal= {arXiv preprint arXiv:1706.09111},
year = {2018}
}
Comments
38 pages. The main results have been improved. This version has been accepted for publication in Mathematical Research Letters