Soliton propagation through a disordered system: statistics of the transmission delay

Sergey A. Gredeskul, Stanislav Derevyanko, Alexander S. Kovalev, Jaroslaw E. Prilepsky

Research output: Contribution to journalArticle

Abstract

We have studied the soliton propagation through a segment containing random pointlike scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method has been developed for obtaining the statistical characteristics of the soliton transmission through the segment. The method is applicable for any classical particle traversing through a disordered segment with the given velocity transformation after each act of scattering. In the case of weak scattering and relatively short disordered segment the transmission time delay of a fast soliton is mostly determined by the shifts of the soliton center after each act of scattering. For sufficiently long segments the main contribution to the delay is due to the shifts of the amplitude and velocity of a fast soliton after each scatterer. Corresponding crossover lengths for both cases of light and heavy solitons have been obtained. We have also calculated the exact probability density function of the soliton transmission time delay for a sufficiently long segment. In the case of weak identical scatterers the latter is a universal function which depends on a sole parameter—the mean number of scatterers in a segment.
Original languageEnglish
Article number036608
JournalPhysical Review E
Volume81
Issue number3
DOIs
Publication statusPublished - 30 Mar 2010

Fingerprint

Disordered Systems
Solitons
solitary waves
statistics
Propagation
Statistics
propagation
scattering
Scattering
Time Delay
time lag
Universal Function
shift
Probability density function
probability density functions
Crossover
crossovers

Bibliographical note

©2010 American Physical Society. Soliton propagation through a disordered system: Statistics of the transmission delay. Sergey A. Gredeskul, Stanislav A. Derevyanko, Alexander S. Kovalev, and Jaroslaw E. Prilepsky
Phys. Rev. E 81, 036608 – Published 30 March 2010

Keywords

  • soliton propagation
  • random pointlike scatterers
  • soliton transmission

Cite this

Gredeskul, Sergey A. ; Derevyanko, Stanislav ; Kovalev, Alexander S. ; Prilepsky, Jaroslaw E. / Soliton propagation through a disordered system : statistics of the transmission delay. In: Physical Review E. 2010 ; Vol. 81, No. 3.
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Soliton propagation through a disordered system : statistics of the transmission delay. / Gredeskul, Sergey A.; Derevyanko, Stanislav; Kovalev, Alexander S.; Prilepsky, Jaroslaw E.

In: Physical Review E, Vol. 81, No. 3, 036608, 30.03.2010.

Research output: Contribution to journalArticle

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