Piston Dispersive Shock Wave Problem

Journal Article · Fri Feb 29 04:00:00 EST 2008 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.100.084504· OSTI ID:21024810

Hoefer, M A ^[1]; Ablowitz, M J ^[2]; Engels, P ^[3]

---

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

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 Schroedinger 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.

• OSTI ID: 21024810
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 8 Vol. 100; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
BIFURCATION
BOSE-EINSTEIN CONDENSATION
NONLINEAR OPTICS
PERIODICITY
PISTONS
SCHROEDINGER EQUATION
SHOCK WAVES
VELOCITY