Nonlinear phenomena in electromagnetic and acoustic wave propagation

We studied mathematical problems in electromagnetic and acoustic wave propagation which involve nonlinear partial differential equations, or linear partial differential equations with random coefficients. A general theory of weakly nonlinear high frequency wave propagation was developed which applies to waves in number of dimensions. It justifies the nonlinearization technique of Whitham and Landau and extends it to interacting waves and to other types of waves. The theory was successfully applied to weak shock diffraction. The theory of wave reflection from rough surfaces was extended to yield the correlation functions of the scattered field. It was found that the second order correlations could be expressed in terms of the reflection coefficient and the differential scattering cross section of the surface.