Parabolic Equation and Pseudodifferential ParabolicEquation Technique

K.V. Avilov and N.E. Mal'tsev, Calculation of sound fields in the ocean by the parabolic equation method, Akust. Zh. vol. 27, 3, pp. 335-340 - acoust-pap81-r.pdf (in Russian, 164 Kb), acoust-pap81-e.pdf (in English, 196 Kb).

K. V. Avilov, The calculation of the harmonic sound fields in the 2D inhomogeneous waveguides by the corrected wide-angle parabolic equation technique, N.N. Andreev Acoustics Institute Report, 1983 - acoust-pap83-r.pdf (in Russian, 347 Kb).

K. V. Avilov, The calculation of the harmonic sound fields in waveguides by the corrected anywide-angle parabolic approximation, in Waves and Diffraction-85, The Allunion Symposium Proceedings, Tbilissi, 1985 - acoust-pap85-r.pdf (in Russian, 98.7 Kb), acoust-pap85-e.pdf (in English, 73.7 Kb).

K. V. Avilov, The one-way propagation approximation in the calculation of the ocean sound fields, in Acoustics of the Ocean Medium, L.M. Brekhovskikh and I.B. Andreeva, Eds, Moscow, Nauka, 1989 - acoust-pap89-r.pdf (in Russian, 380 Kb).

K.V. Avilov, An Effective Numerical Solution of Guided Waves Equations, Journal de Physique IV, Colloque C1, supplement au Journal de Physique III, Vol. 2, avril 1992 - acoust-pap92-e.pdf (in English, 183 Kb).

K. V. Avilov, Additive factorization + Pade approximations = effective underwater sound calculations, in Aspects Recent de l'Acoustique Sous-Marine Russe, M. Galactionov, Ed., Editions de l'IFREMER, Brest, France, 1994 - acoust-pap94-e.pdf (in English, 214 Kb), acoust-pap94-f.pdf (in French, 590 Kb).

K. V. Avilov, Pseudodifferential Parabolic Equations of Sound Propagation in the Slowly Range-Dependent Ocean and Their Numerical Solutions, Akust. Zh., Vol. 41, no. 1, 1995, pp. 5-12 - acoust-pap95-r.pdf (in Russian, 286 Kb), acoust-pap95-e.pdf (in English, 278 Kb).

K.V. Avilov and O.E. Popov, The Calculation of the Signal from a Broadband Point Source Arbitrarily Moving in the Range-Dependent Ocean, in Ocean Acoustics, Proceedings of the L.M. Brekhovskikh Symposium, Moscow, GEOS, 1998 - acoust-pap98-r.pdf (in Russian, 150 Kb), acoust-pap98-e.pdf (in English, 104 Kb).

The PDPE section in the PE department of the Ocean Acoustics Library.

Some examples and verifications

S. V. Burenkov and O. E. Popov, Modeling of mode interaction in a two-dimensionally inhomogeneous waveguide, Akust. Zh., vol. 35, pp. 590-595 - acoust-examples1-r.pdf (in Russian, 279 Kb), acoust-examples1-e.pdf (in English, 236 Kb).

Some examples of calculation results from PDPE - acoust-examples2-r.pdf (in Russian, 257 Kb), acoust-examples2-e.pdf (in English, 479 Kb).