100 citations · 128 across the 14 of their papers we have counts for
14 papers
General superpositions of Gaussian beams and propagation errors
Hailiang Liu, James Ralston, Peimeng Yin
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful…
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…
Gauge Equivalence and the Inverse Spectral Problem for the Magnetic Schrödinger Operator on the Torus
Gregory Eskin, Jim Ralston
We study the inverse spectral problem for the Schrödinger operator on the two-dimensional torus with even magnetic field and even electric potential . V.Guillemin…
Gaussian Beam Methods for the Helmholtz Equation
Hailiang Liu, James Ralston, Olof Runborg +1
In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of non-trapping rays we s…
The Aharonov-Bohm effect in spectral asymptotics of the magnetic Schrödinger operator
Gregory Eskin, James Ralston
We show that in the absence of a magnetic field the spectrum of the magnetic Schrödinger operator in an annulus depends on the cosine of the flux associated with the magnetic poten…
Remark on Spectral Rigidity for Magnetic Schrödinger Operators
Gregory Eskin, James Ralston
We give a simple proof of Guillemin's theorem on the determination of the magnetic field on the torus by the spectrum of the corresponding Schrödinger operator.