Tutorial II. On the Gaussian Beam Approximation, Part I: Gaussian Beam Approximations for Initial Value Problems for Hyperbolic Systems

James Ralston
UCLA
Mathematics

Unlike conventional geometrical optics, the Gaussian beam Ansatz gives approximate solutions to PDE which are concentrated on a single ray path. They do not develop singularities in finite time. However, using superposition over families of rays, they provide an accurate approximation to solutions with caustics and more general singularities.


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