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

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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.

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Authors and Affiliations

  1. Humboldt University, Berlin, Germany

    J. Brüning

  2. Institute for Problems of Mechanics, RAS, Moscow, Russia

    S. Yu. Dobrokhotov, R. V. Nekrasov & A. I. Shafarevich

Authors
  1. J. Brüning
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  2. S. Yu. Dobrokhotov
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  3. R. V. Nekrasov
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  4. A. I. Shafarevich
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Correspondence to J. Brüning.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 215–235, May, 2008.

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Brüning, J., Dobrokhotov, S.Y., Nekrasov, R.V. et al. Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity. Theor Math Phys 155, 689–707 (2008). https://doi.org/10.1007/s11232-008-0059-y

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  • DOI: https://doi.org/10.1007/s11232-008-0059-y

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