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Oblique spatial dispersive shock waves in nonlinear Schrodinger flows

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journal contribution
posted on 07.04.2017, 09:18 by M.A. Hoefer, Gennady El, A.M. Kamchatnov
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.

Funding

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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

SIAM Journal on 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.

Publisher

© Society for Industrial and Applied Mathematics

Version

NA (Not Applicable or Unknown)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

21/03/2017

Publication date

2017

Notes

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

ISSN

0036-1399

eISSN

1095-712X

Language

en

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