Abstract:
We develop a method for computing the Gaussian beam solution for a general class of symmetric hyperbolic systems in both Lagrangian and Eulerian frames. Symmetric hyperbolic systems include many physically relevant systems of partial differential equations (PDE) such as Maxwell's equations, the elastic equations and the acoustic equations. We extend the Gaussian beam method to the regime of symmetric hyperbolic systems with constant degeneracy. Finally I will discuss the interesting potential for this method to handle non-constant degeneracy and eigenvalue crossing points in the hyperbolic systems and SchrÃ¶dinger equation cases. |