Geodesic
Propagation of Gaussian wave packets in thin periodic quantum
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 215-235

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We consider the nonlinear Schrödinger equation with an integral Hartree-type nonlinearity in a thin quantum waveguide and study the propagation of Gaussian wave packets localized in the spatial variables. In the case of periodically varying waveguide walls, we establish the relation between the behavior of wave packets and the spectral properties of the auxiliary periodic problem for the one-dimensional Schrödinger equation. We show that for a positive value of the nonlinearity parameter, the integral nonlinearity prevents the packet from spreading as it propagates. In addition, we find situations such that the packet is strongly focused periodically in time and space.
Keywords: nonstationary Schrödinger equation with an integral nonlinearity, thin tube, Gaussian wave packet, localization. 
@article{TMF_2008_155_2_a2,
     author = {J. Br\"uning and S. Yu. Dobrokhotov and R. V. Nekrasov and A. I. Shafarevich},
     title = {Propagation of {Gaussian} wave packets in thin periodic quantum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {215--235},
     publisher = {mathdoc},
     volume = {155},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a2/}
}
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J. Brüning; S. Yu. Dobrokhotov; R. V. Nekrasov; A. I. Shafarevich. Propagation of Gaussian wave packets in thin periodic quantum. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 215-235. http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a2/