Higher-order parabolic approximations to time-independent wave equations

DOI10.1063/1.525978zbMath0548.35027OpenAlexW1995196743MaRDI QIDQ3341236

Robert J. Krueger, James Corones

Publication date: 1983

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525978

zbMATH Keywords

elastic wave equationinhomogeneous mediumreduced wave equationhigher-order parabolic approximations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Vibrations in dynamical problems in solid mechanics (74H45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Wave splitting and the reflection operator for the wave equation in R3 ⋮ Factorization of the wave equation in higher dimensions ⋮ Factorization of the wave equation in a nonplanar stratified medium ⋮ Splitting methods and invariant imbedding for time-independent wave propagation in focusing media and wave guides ⋮ Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations ⋮ Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation ⋮ A comparison of parabolic wave theories for linearly elastic solids ⋮ Splitting methods for time-independent wave propagation in random media

Cites Work

• Generalizations of the Bremmer series based on physical concepts
• Parabolic approximations to the time-independent elastic wave equation
• The W.K.B. approximation as the first term of a geometric‐optical series