Volume 16, Issue 1, March 2013, Pages 35 - 45
Geometrization of the Leading Term in Acoustic Gaussian Beams
Matias F. Dahlmatias.firstname.lastname@example.org
Institute of Mathematics, P. O. Box 1100, 02015 Helsinki, Finland, email@example.com
Received 10 January 2008, Accepted 15 April 2008, Available Online 7 January 2021.
- https://doi.org/10.1142/S1402925109000042How to use a DOI?
- Gaussian beams, wave packets, asymptotic analysis, wave equation, conservation of energy, leading amplitude term
We study Gaussian beams for the wave equation on a Riemannian manifold. For the transport equation we geometrize the leading term at the center of the Gaussian beam. More precisely, ifis a Gaussian beam propagating along a geodesic c, then we show that where C is a constant and Y is a complex Jacobi tensor. Using a constant of motion for the non-linear Riccati equation related to the Jacobi equation, we prove that asymptotically the leading term of the energy carries constant energy.
- © 2009 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Matias F. Dahl PY - 2021 DA - 2021/01 TI - Geometrization of the Leading Term in Acoustic Gaussian Beams JO - Journal of Nonlinear Mathematical Physics SP - 35 EP - 45 VL - 16 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000042 DO - https://doi.org/10.1142/S1402925109000042 ID - Dahl2021 ER -