Speaker：LAN Yang，University of
Place：Room 1518, School of
Detail：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 Raphaël.
Organizer: School of Mathematical Sciences