中科院数学与系统科学研究院
数学研究所
华罗庚数学重点实验室
华罗庚青年数学论坛
综合报告
报告人： Lan Yang（Universit？t Basel）
题 目：On asymptotic dynamics for $L^2$-critical gKdV with saturated perturbations
时 间：2019.07.09（星期二），10:45-11:45
地 点：数学院南楼N224室
Abstract : W？e consider the $L^2$ critical gKdV equation with a saturated perturbation. ？In this case, all $H^1$ solution ？are？ global ？in time. ？Our goal is to classify the ？asymptotic ？dynamics ？for solutions with initial data ？near ？the ground state. Together with a suitable decay assumption, there are only three possibilities: (i) the solution converges asymptotically to a solitary wave, whose $H^1$ norm is of size $\gamma^{-2/(q-1)}$, as $\gamma\rightarrow0$; (ii) the solution is always in a small neighborhood of the modulated family of solitary waves, but blows down at $+\infty$; (iii) the solution leaves any small neighborhood of the modulated family of the solitary waves.？ ？This extends the result of classification of the rigidity dynamics near the ground state for the unperturbed $L^2$ critical gKdV (corresponding to $\gamma=0$) by Martel, Merle and Rapha\"el. It also provides a way to consider the continuation properties after blow-up time for $L^2$-crtitical gKdV equations.
