Abstract. A new method of solution is proposed for solution of the wave equation in one space dimension \new{with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an infinite series of integrals, where the integrand involves only the initial data and the PDE coefficients. Each term in the series represents the influence of paths with a fixed number of turning points.
NOTE: This paper is a revised version of our earlier paper "A characteristics-based approximation for wave scattering from an arbitrary obstacle in one dimension" after incorporating comments from the reviews, which included the suggestion of retitling it. The revised manuscript has now been published:
Journal webpage ... M123863.pdf
bibtex entry:
@article{GeorgeKetchesonLeVeque2019c,
author = {J. D. George and D. I. Ketcheson and R. J. LeVeque},
title = {A path integral method for solution of the wave equation with
continuously-varying coefficients},
journal = "SIAM J. Appl. Math.",
pages = {2615-2638},
volume = {79},
year = {2019},
doi = {10.1137/19M1238630}
}