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Title: Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
Authors: El, G.A.
Nguyen, Khiem
Smyth, Noel F.
Issue Date: 2018
Publisher: © IOP Publishing Ltd & London Mathematical Society
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.
Abstract: 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.
Description: 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
Sponsor: 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].
Version: Accepted for publication
DOI: 10.1088/1361-6544/aaa10a
URI: https://dspace.lboro.ac.uk/2134/27781
Publisher Link: https://doi.org/10.1088/1361-6544/aaa10a
ISSN: 0951-7715
Appears in Collections:Published Articles (Maths)

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