Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term

Autor:	Kishimoto, Nobu, Tsutsumi, Yoshio
Rok vydání:	2017
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 38 pages. The main results have been improved. This version has been accepted for publication in Mathematical Research Letters
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1706.09111 Zobrazit plný text záznamu View this record from Arxiv