Piston Dispersive Shock Wave Problem

M. A. Hoefer, M. J. Ablowitz, and P. Engels

Phys. Rev. Lett. 100, 084504 – Published 28 February 2008

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.

Received 24 October 2007

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

Authors & Affiliations

M. A. Hoefer^1,*, M. J. Ablowitz², and P. Engels³

¹National Institute of Standards and Technology, Boulder, Colorado 80305, USA
²Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
³Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA

^*hoefer@boulder.nist.gov

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Vol. 100, Iss. 8 — 29 February 2008

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