Presentation title: “On the two different approaches to the derivation of parabolic equations”
(The 1st lecture of the series of “Parabolic equations: standard theory vs iterative parabolic approximations”)
Presenter: Dr. Pavel S. Petrov
Time: 15:00-16:30, July 5, 2018
Location: Academic lecture hall on the 15th floor of the Underwater Acoustic Engineering Building
Short Bio of the presenter:
Pavel S. Petrov received his Master’s degree in Mathematics from Irkutsk State University, Russia; and his Doctorate degree in Theoretical Physics from Il’ichev Pacific Oceanological Institute, Russia. From 2012, Dr. Pavel S. Petrov is a Researcher in Il’ichev Pacific Oceanological Institute, and also an adjunct Associate Professor in Far Eastern Federal University. He has received the Humboldt Research Fellowships twice, and went to Universities in German as a visiting scholar. He also worked as a short-term post-doctoral researcher in University of Haifa, Israel, collaborating with Professor Boris Katsnelson. Dr. Pavel S. Petrov received the Illychef Prize for Young Scientists in Acoustics and Ocean Research from Il’ichev Pacific Oceanological Institute in 2017, due to the series of high-level papers on 3-dimension sound prorogation models his published.
The research focuses of Dr. Pavel S. Petrov includes acoustic propagation, absorption and scattering, computational ocean acoustics, mathematical modeling of wave processes, asymptotic methods and so on. Dr. Pavel S. Petrov has made significant contributions to the 3- dimensional ocean sound propagation and applications. Several programing codes on 3-dimensional sound field calculation written by him has been uploaded to the famous open-source website on underwater acoustics – Ocean Acoustics Library, which can be downloaded for free.
Abstract of the presentation:
The historical overview of different techniques for the derivation of paraxial propagation equations (or parabolic equations) is given, and the original motivation from radio-waves theory is outlined. The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways of the wide-angle parabolic equation derivation. Advantages and disadvantages of both derivation methods are discussed. The interface and boundary conditions for both cases are considered in the context of acoustical applications. Two classical problems of underwater acoustics are considered. A convergence theorem for the iterative parabolic equation is proven. It is shown that the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle the case of nonlinear Helmholtz equation. The nonlinear iterative parabolic approximations for the wave propagation in (optical) Kerr media are presented. An example demonstrating the capability of iterative parabolic equations to take non-paraxial propagation effects in nonlinear media into account is considered.
