## 偏微分方程式セミナー(2014/6/9)： Stability of line standing waves near the bifurcation point for nonlinear Sch\”odinger equation, 山崎陽平氏 (京都大学)

2014年 　 6月 9日 16時 30分 ～ 2014年 　 6月 9日 17時 30分

We consider the transverse instability for nonlinear Schr\"odinger
equation. One dimensional nonlinear Schr\"odinger equation has a stable standing
wave. Here, we regard this standing wave as a line standing wave of two
dimensional nonlinear Schr\"odinger equation with the periodic boundary
condition in the transverse direction with the period $2\pi L$.
Rousset and Tzvetkov showed that there exists the critical period $2\pi L_*$ such that the line standing wave is stable for $L < L_*$ and the
line standing wave is unstable for $L > L_*$.
In this talk, we will present the transverse instability in the
degenerate case $L=L_*$ and the relation between the stability and the
bifurcation.