Two systems of hyperbolic equations, arising in the multiphase semiclassical limit of the linear Schrödinger equations, are investigated. One stems from a Wigner measure analysis and uses a closure by the Delta functions, whereas the other relies on the classical WKB expansion and uses the Heaviside functions for closure. The two resulting moment systems are weakly and non-strictly hyperbolic respectively. They provide two different Eulerian methods able to reproduce superimposed signals with a finite number of phases. Analytical properties of these moment systems are investigated and compared. Efficient numerical discretizations and test-cases with increasing difficulty are presented.
|Original language||English (US)|
|Number of pages||35|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - Dec 1 2003|
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- Applied Mathematics