Solitons in fluctuating hydrodynamics of diffusive processes

Alexios P. Polychronakos
Phys. Rev. E 101, 022209 – Published 14 February 2020

Abstract

We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the symmetric exclusion process (SEP). We show that the two fluid systems are related by a nonlinear transformation but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, whereas sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.

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  • Received 21 November 2019
  • Revised 7 January 2020
  • Accepted 29 January 2020

DOI:https://doi.org/10.1103/PhysRevE.101.022209

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsStatistical Physics & ThermodynamicsNonlinear Dynamics

Authors & Affiliations

Alexios P. Polychronakos*

  • Department of Physics, The City College of New York, New York 10031, USA and The Graduate Center, CUNY, New York, New York 10016, USA

  • *apolychronakos@ccny.cuny.edu

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Issue

Vol. 101, Iss. 2 — February 2020

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