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DATE | 2019-02-21 15:10-16:00 |

PLACE | 數學館3174教室 |

SPEAKER | Yoshio Tsutsumi 教授（京都大學） |

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

ABSTRACT |
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., [1]). 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 [2] with Nobu Kishimoto, RIMS, Kyoto University. References
[1] G. Agrawal, Nonlinear Fiber Optics, 4th edition, Elsevier / Academic Press, Burlington, 2007.
[2] N. Kishimoto and Y. Tsutsumi, Ill-posedness of the third order NLS equation with Raman scattering term, preprint, arXiv: 1706.09111v1 [math.AP]
演講簡報 |