Communications in Mathematical Sciences

Volume 16 (2018)

Number 6

Wave propagation in random waveguides with long-range correlations

Pages: 1557 – 1596



Christophe Gomez (Aix Marseille Université, CNRS, Centrale Marseille, France)

Knut Sølna (Department of Mathematics, University of California at Irvine)


The paper presents an analysis of acoustic wave propagation in a waveguide with random fluctuations of its sound speed profile. These random perturbations are assumed to have long-range correlation properties. In the waveguide, a monochromatic wave can be decomposed in propagating modes and evanescent modes, and the random perturbation couples all these modes. The paper presents an asymptotic analysis of the mode-coupling mechanism and uses this to characterize the transmitted wave. The paper presents the first fully rigorous characterization of wave propagation in long-range non-layered media.


acoustic waveguides, random media, asymptotic analysis, long-range correlations

2010 Mathematics Subject Classification

35Q99, 60F05, 76B15

Received 10 May 2016

Accepted 18 March 2018

Published 7 February 2019