Nonlinear wave propagation in a disordered medium

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In this paper we consider the problem of solitary wave propagation in a weakly disordered potential. Through a series of careful numerical experiments we have observed behavior which is in agreement with the theoretical predictions of Kivshar et al., Bronski, and Garnier. In particular we observe numerically the existence of two regimes of propagation. In the first regime the mass of the solitary wave decays exponentially, while the velocity of the solitary wave approaches a constant. This exponential decay is what one would expect from known results in the theory of localization for the linear Schrödinger equation. In the second regime, where nonlinear effects dominate, we observe the anomalous behavior which was originally predicted by Kivshar et al. In this regime the mass of the solitary wave approaches a constant, while the velocity of the solitary wave displays an anomalously slow decay. For sufficiently small velocities (when the theory is no longer valid) we observe phenomena of total reflection and trapping.

Original languageEnglish (US)
Pages (from-to)995-1015
Number of pages21
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Sep 1998
Externally publishedYes


  • Disordered media
  • Nonlinear scattering
  • Nonlinear schrödinger equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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