100 citations · 128 across the 14 of their papers we have counts for
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A Grazing Gaussian Beam
James Ralston, Neelesh Tiruviluamala
We consider Friedlander's wave equation in two space dimensions in the half-space x > 0 with the boundary condition u(x,y,t)=0 when x=0. For a Gaussian beam w(x,y,t;k) concentrated…
Recovery of high frequency wave fields for the acoustic wave equation
Hailiang Liu, James Ralston
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotic…
Recovery of high frequency wave fields from phase space based measurements
Hailiang Liu, James Ralston
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotic…
Inverse Scattering for Gratings and Wave Guides
Gregory Eskin, James Ralston, Masahiro Yamamoto
We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes…
Inverse spectral problems in rectangular domains
Gregory Eskin, James Ralston
We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potenti…
Inverse boundary value problems for systems of partial differential equations
Gregory Eskin, James Ralston
We describe a simple way of constructing exponentially growing solutions of the second order systems with the Laplacian as the principal term.