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Article overview
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The piston dispersive shock wave problem | | M. A. Hoefer
; M. J. Ablowitz
; P. Engel
; | | Date: |
14 Oct 2007 | | Abstract: | The one-dimensional piston shock problem is a classical result of shock wave
theory. In this work, the analogous dispersive shock wave (DSW) problem for a
dispersive fluid described by the nonlinear Schr"odinger equation is analyzed.
Asymptotic solutions are calculated using Whitham averaging theory for a
"piston" (step potential) moving with uniform speed into a dispersive fluid at
rest. These asymptotic results agree quantitatively with numerical simulations.
It is shown that the behavior of these solutions is quite different from their
classical counterparts. In particular, the shock structure depends on the speed
of the piston. These results have direct application to Bose-Einstein
condensates and the propagation of light through a nonlinear, defocusing
medium. | | Source: | arXiv, 0710.2634 | | Services: | Forum | Review | PDF | Favorites | |
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