Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | Dr. Kexin Jin ，Princeton university and Tsinghua university
| | Inviter: | | Title:
| Long time dynamics of the NLS | Time & Venue:
| 2021.12.06 10:00-11:00 N210室 | Abstract:
| We prove a vanishing property of the normal form transformation of the 1D cubic nonlinear Schr\"odinger (NLS) equation with periodic boundary conditions on $[0,L]$. We apply this property to quintic resonance interactions and obtain a description of dynamics for time up to $T=\frac{L^2}{\epsilon^4}$, if $L$ is sufficiently large and size of initial data $\epsilon$ is small enough. Since $T$ is the characteristic time of wave turbulence, this result implies the absence of wave turbulence behavior of 1D cubic NLS. Joint with Xiao Ma.
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