Maslov's Canonical Operator in Problems on Localized Asymptotic Solutions of Hyperbolic Equations and Systems

2019 ◽  
Vol 106 (3-4) ◽  
pp. 402-411 ◽  
Author(s):  
V. E. Nazaikinskii ◽  
A. I. Shafarevich
Keyword(s):  
Hyperbolic Equations ◽  
Asymptotic Solutions ◽  
Canonical Operator ◽  
Maslov’S Canonical Operator

UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS

2001 ◽  
Vol 09 (02) ◽  
pp. 495-513 ◽  
Author(s):  
A. HANYGA ◽  
M. SEREDYŃSKA
Keyword(s):  
Asymptotic Solution ◽  
Frequency Domain ◽  
Singular Integral ◽  
Hyperbolic Equations ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Asymptotic Solutions ◽  
Convolution Operators ◽  
Pseudodifferential Equations

Uniformly asymptotic frequency-domain solutions for a class of hyperbolic equations with singular convolution operators are derived. Asymptotic solutions for this class of equations involve additional parameters — called attenuation parameters — which control the smoothing of the wavefield at the wavefront. At caustics the ray amplitudes have a singularity associated with vanishing of ray spreading and with divergence of an integral controlling the rate of exponential amplitude decay. Both problems are resolved by applying a generalized Kravtsov–Ludwig formula derived in this paper. A different asymptotic solution is constructed in the case of separation of dispersion and focusing effects.

New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems

2015 ◽  
Vol 92 (2) ◽  
pp. 548-553 ◽  
Author(s):  
A. I. Allilueva ◽  
S. Yu. Dobrokhotov ◽  
S. A. Sergeev ◽  
A. I. Shafarevich
Keyword(s):  
Hyperbolic Systems ◽  
Asymptotic Solutions ◽  
Maslov Canonical Operator ◽  
Canonical Operator
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