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On asymptotic dynamics for L^2 critical generalized KdV equations with a saturated perturbation
On asymptotic dynamics for L^2 critical generalized KdV equations with a saturated perturbation
教师介绍

本讲教师:兰洋
所属学科:理科
人  气:473

课程介绍
摘要:We consider the $L^2$ critical gKdV equation with a saturated perturbation. For any initial data in $H^1$, the corresponding solution is always global and bounded in $H^1$. This equation has a family of solitons, and our goal is to study the behavior of solutions with initial data near the soliton. Together with a suitable decay assumption, there are only 3 possibilities: i. the solution converges asymptotically to a solitary wave; ii. the solution is always in a small neighborhood of the modulated family of solitary waves, but blows down at infinite time; iii. the solution leaves any small neighborhood of the modulated family of the solitary waves. This result can be viewed as a perturbation of the rigidity dynamics near ground state for $L^2$ critical gKdV equations proved by Martel, Merle and Rapha?l.

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