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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/24663

Title: Oblique spatial dispersive shock waves in nonlinear Schrodinger flows
Authors: El, G.A.
Hoefer, M.A.
Kamchatnov, A.M.
Issue Date: 2017
Publisher: Society for Industrial and Applied Mathematics
Citation: EL, G.A., HOEFER, M.A. and KAMCHATNOV, A.M., 2017. Oblique spatial dispersive shock waves in nonlinear Schrodinger flows. SIAM Journal on Applied Mathematics, In Press.
Abstract: In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schrodinger boundary value problems. Self-similar, simple wave solutions of the modulation equations yield relations between the DSW’s orientation and the upstream/downstream flow fields. Time dependent numerical simulations demonstrate a convective or absolute instability of oblique DSWs in supersonic flow over obstacles. The convective instability results in an effective stabilization of the DSW.
Description: This paper is closed access until it is published.
Sponsor: M.A.H. was partially supported by NSF CAREER DMS-1255422 and DMS-1008973. A.M.K. was partially supported by RFBR grant No. 16-01-00398.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/24663
Publisher Link: https://www.siam.org/journals/siap.php
ISSN: 0036-1399
Appears in Collections:Closed Access (Maths)

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