Representation of high frequency wave fields in the form of integrals over Gaussian beams. Gaussian beams are solutions of corresponding hyperbolic equations or system of equations, which have the ray type asymptotic expansion with complex phase and concentrated in a neighbourhood of a geodesic. The integral representations over Gaussian beams give uniform asymptotic expansions of high frequency wave fields on any compact set. The representations are convenient for calculation both in regulare zone of the geodesic fields and in singular points of the fields. Solution of inverse problem of determination of parameters of different media by boundary measurements. Method is based upon construction of a geometric model which is equivalent to initial physical model and uses Gaussian beams.
Main publications:
Katchalov A., Kurylev Y. Multidimensional inverse problems with incomplete boundary spectral data // Comm. in PDE, 1998, 23, no. 1–2, 55–95.
Katchalov A., Kurylev Y., Lassas M. Inverse boundary spectral problems. 2001, CRC Press, 290 p.
