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Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

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posted on 14.12.2017 by Gennady El, Khiem Nguyen, Noel F. Smyth
We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal BenjaminOno type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.

Funding

The work of L.T.K.N was supported by the Ruhr University Research School PLUS, funded by Germany’s Excellence Initiative [DFG GSC 98/3].

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Citation

EL, G.A., NGUYEN, K. and SMYTH, N.F., 2018. Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type. Nonlinearity, 31(4), pp. 1392-1416.

Publisher

© IOP Publishing Ltd & London Mathematical Society

Version

AM (Accepted Manuscript)

Acceptance date

11/12/2017

Publication date

2018-02-27

Notes

This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aaa10a

ISSN

0951-7715

eISSN

1361-6544

Language

en

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