Two moment systems for computing multiphase semiclassical limits of the schrödinger equation

Laurent Gosse, Shi Jin, Xiantao Li

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)1689-1723
Number of pages35
JournalMathematical Models and Methods in Applied Sciences
Volume13
Issue number12
DOIs
StatePublished - Dec 1 2003

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

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