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Title: Refraction of dispersive shock waves
Authors: El, G.A.
Khodorovskii, V.V.
Leszczyszyn, Antin M.
Keywords: Dispersive shock wave
Euler-Poisson-Darboux equation
Nonlinear wave interactions
Rarefaction wave
Whitham equations
Issue Date: 2012
Publisher: © Elsevier
Citation: EL, G.A., KHODOROVSKII, V.V. and LESZCZYSZYN, A.M., 2012. Refraction of dispersive shock waves. Physica D: Nonlinear Phenomena, 241 (18), pp.1567-1587.
Abstract: We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.
Description: This is the author’s version of a work that was accepted for publication in Physica D: Nonlinear Phenomena. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.physd.2012.06.002
Version: Accepted for publication
DOI: 10.1016/j.physd.2012.06.002
URI: https://dspace.lboro.ac.uk/2134/16946
Publisher Link: http://dx.doi.org/10.1016/j.physd.2012.06.002
ISSN: 0167-2789
Appears in Collections:Published Articles (Maths)

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