2025_programme: Wavefronts deformation by parabolic equations

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  • Day: June 19, Thursday
      Location / Time: B. ERATO at 18:00-18:20
  • Last minutes changes: -
  • Session: 01. Acoustics in Ocean Observation Systems
    Organiser(s): Jaroslaw Tegowski, Philippe Blondel, Hanne Sagen
    Chairperson(s): Jaroslaw Tegowski, Philippe Blondel
  • Lecture: Wavefronts deformation by parabolic equations
    Paper ID: 2260
    Author(s): Alena Zakharenko, Pavel Petrov
    Presenter: Pavel Petrov
    Abstract: Theory of iterative parabolic equations (itPEs) originating from the works of Malyuzhinets has been recently recently found to be a useful tool for modeling propagation of guided waves in underwater acoustics and nonlinear optics. The main problem arising in practical computations with itPEs is the presence of non-physical sidelobes in the solution when the itrative parabolic approximation is constructed in the from of a Taylor series. It was recently observed that this issue can be resolved by constructing iterative Pade approximations. In this talk the properties of both types of iterative approximations are investigated by studying respective wavefronts in comparison with wavefronts of the fundamental solution of Helmholtz equation. Such comparison provides a new explanation of the well-known fact that Pade expansions are in principle more efficient way to derive parabolic equations than their Taylor counterparts.
  • Corresponding author: Prof Pavel Petrov
    Affiliation: Instituto de Matemática Pura e Aplicada
    Country: Brazil

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