Piston dispersive shock wave problem

M A Hoefer; M J Ablowitz; P Engels

doi:10.1103/PhysRevLett.100.084504

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Piston dispersive shock wave problem

M A Hoefer, M J Ablowitz and P Engels

Physical review letters, Vol.100(8), pp.084504-084504

02/29/2008

DOI: https://doi.org/10.1103/PhysRevLett.100.084504

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https://hdl.handle.net/2376/108763

PMID: 18352629

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Abstract

The piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schrödinger equation is analyzed. Asymptotic solutions are calculated for a piston (step potential) moving with uniform speed into a dispersive fluid at rest. In contrast to the classical case, there is a bifurcation of shock behavior where, for large enough piston velocities, the DSW develops a periodic wave train in its wake with vacuum points and a maximum density that remains fixed as the piston velocity is increased further. These results have application to Bose-Einstein condensates and nonlinear optics.

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Title: Piston dispersive shock wave problem
Creators: M A Hoefer - National Institute of Standards and Technology, Boulder, Colorado 80305, USA. hoefer@boulder.nist.gov
M J Ablowitz
P Engels
Publication Details: Physical review letters, Vol.100(8), pp.084504-084504
Academic Unit: Physics and Astronomy, Department of
Publisher: United States
Identifiers: 99900547256901842
Language: English
Resource Type: Journal article