In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements. Computational results dem...

We consider the Cauchy problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of the high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first di...

We consider the problem of high-frequency asymptotics for the time-dependent onedimensional Schrödinger equation with rapidly oscillating initial data. This problem is commonly studied via the WKB method. An alternative method is based on the limit Wigner measure. This approach recovers geometrical optics, but, like the WKB method, it fails at caustics. To remedy this deficiency we employ the s...

A geometrical optics method for solving wave propagation in dispersive weakly nonlinear, weakly inhomogeneous media is applied to plasmas. In the case that the dispersion is comparable to the nonlinearity, the method yields the expected soliton solutions. For strong dispersion, it is found that the amplitude has the same form as in the linear case except that it is multiplied by a slow varying ...

Abstract. The gravitational lensing of gravitational waves should be treated in the wave optics instead of the geometrical optics when the wave length λ of the gravitational waves is larger than the Schwarzschild radius of the lens mass M. The wave optics is based on the diffraction integral which represents the amplification of the wave amplitude by lensing. We study the asymptotic expansion o...