Math. Phys. Seminar

[Boris Dubrovin]

				Mathematical Physics Seminar

Friday, November 23, at 14:30 - 15:30, Room C of SISSA Main Building

				Prof. S.Dobrokhotov

Institute for Problems in Mechanics of Russian Academy of Sciences

&  Dept. of Nanotechnology and Informatics
of Moscow Institute of Physics and Technology

		Propagation of Gaussian wave packets
in quantum thin  periodic waveguides with nonlocal Hartree-type  
nonlinearity

Abstract

We consider nonlinear Schroedinger equation with an integral Hartree- 
type nonlinearity in thin waveguide. We study propagation of Gaussian  
wave packets localized in the space. In the case of periodically  
changing walls of the waveguide we establish the relationship between  
the behavior of wave packets and spectral properties of some  
additional 1-D periodic linear Sturm-Liouville problem. We show that  
in the case of positive nonlinear term in contrary  to linear  
situation  the wave packets may not spread. Moreover we show that the  
wave packets can be periodically focused in space and time depending  
on the spectrum of the mentioned 1-D periodic problem.  This work was  
done jointly with J.Bruening, R.Nekrasov and A.Shafarevich).