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Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium

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Abstract

This is the first study of one of the transmission problems associate to the non-linear Schrödinger equation with a random potential. We show that for almost every realization of the medium the rate of transmission vanishes when increasing the size of the medium; however, whereas it decays exponentially in the linear regime, it decays polynomially in the nonlinear one.

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Authors and Affiliations

  1. Laboratoire du CNRS LP 014, école Polytechnique, Centre de Physique Théorique, F-91128, Palaiseau, France

    Pierre Devillard & Bernard Souillard

Authors
  1. Pierre Devillard
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  2. Bernard Souillard
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Additional information

This work is part of a Thèse de Troisième Cycle by P. Devillard.(6)

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Devillard, P., Souillard, B. Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium. J Stat Phys 43, 423–439 (1986). https://doi.org/10.1007/BF01020646

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  • DOI: https://doi.org/10.1007/BF01020646

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