An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
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.
Hoefer, M.
, Ablowitz, M.
and Engels, P.
(2008),
The piston dispersive shock wave problem, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=32816
(Accessed May 30, 2023)