|SPEAKER||Yoshio Tsutsumi 教授（京都大學）|
|TITLE||Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term|
We consider the ill-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus.
It has been universally used among physicists as a mathematical model for the photonic crystal fiber oscillator (see, e.g., ). I show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map at the origin under slightly different conditions, respectively. Physicists sometimes propose models which have strong instability from a mathematical point of view. Equation (1) is such a kind of example and it is not very clear what role the mathematical ill-posedness plays in physics. I also talk about the local unique existence of solutions in the analytic function space.
This talk is based on the joint work  with Nobu Kishimoto, RIMS, Kyoto University. References
 G. Agrawal, Nonlinear Fiber Optics, 4th edition, Elsevier / Academic Press, Burlington, 2007.
 N. Kishimoto and Y. Tsutsumi, Ill-posedness of the third order NLS equation with Raman scattering term, preprint, arXiv: 1706.09111v1 [math.AP]