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Title: Oblique spatial dispersive shock waves in nonlinear Schrodinger flows
Authors: Hoefer, M.A.
El, G.A.
Kamchatnov, A.M.
Issue Date: 2017
Publisher: © Society for Industrial and Applied Mathematics
Citation: HOEFER, M.A., EL, G.A. and KAMCHATNOV, A.M., 2017. Oblique spatial dispersive shock waves in nonlinear Schrodinger flows. SIAM Journal on Applied Mathematics, 77(4), pp.1352-1374.
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 was published in the journal SIAM Journal on Applied Mathematics and the definitive published version is available at https://doi.org/10.1137/16M108882X
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: Published version
DOI: 10.1137/16M108882X
URI: https://dspace.lboro.ac.uk/2134/24663
Publisher Link: https://doi.org/10.1137/16M108882X
ISSN: 0036-1399
Appears in Collections:Published Articles (Maths)

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