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Oblique spatial dispersive shock waves in nonlinear Schrodinger flows
journal contribution
posted on 2017-04-07, 09:18 authored by M.A. Hoefer, Gennady El, A.M. KamchatnovIn 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 MathematicsCitation
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 MathematicsVersion
- 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
2017-03-21Publication date
2017Notes
This paper was published in the journal SIAM Journal on Applied Mathematics and the definitive published version is available at https://doi.org/10.1137/16M108882XISSN
0036-1399eISSN
1095-712XPublisher version
Language
- en