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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 2, Pages 215–235
DOI: https://doi.org/10.4213/tmf6206 (Mi tmf6206) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

J. Brüninga, S. Yu. Dobrokhotovb, R. V. Nekrasovb, A. I. Shafarevichb

a Humboldt University
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
Full-text PDF (741 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf6206
Abstract: 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.
Received: 03.07.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 2, Pages 689–707
DOI: https://doi.org/10.1007/s11232-008-0059-y
Bibliographic databases:
Language: Russian
Citation: J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, A. I. Shafarevich, “Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity”, TMF, 155:2 (2008), 215–235; Theoret. and Math. Phys., 155:2 (2008), 689–707
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:84
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