Small-amplitude solutions for space-multidimensional hamiltonian PDFs under periodic boundary conditions and the modulational instability
- Small-amplitude solutions for space-multidimensional hamiltonian PDFs under periodic boundary conditions and the modulational instability
- 2017-11-23 16:00-17:00
- Sergei Kuksin
I will discuss the problem of studying the long-time behaviour of samll solutions for nornlinear Hamiltonian PDEs on T^d. I will explain that the equations in question have abundance of small time-quasiperiodic solutions and that the behaviour of solution for space-multidimensional equations (d>1) significantly differs from that for the 1d systems since in the 1d case the constructed solutions are linearly stable, while in the space-multidimensional case many of them are linearly unstable. Physicists call this phenomenon the modulational instability.
The talk is base on my recent joint work with H.Eliasson and B.Grebert in GAFA 26(2016). (arCiv 1604.01657)