UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS
2001 ◽
Vol 09
(02)
◽
pp. 495-513
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Keyword(s):
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.
2009 ◽
Vol 7
(1)
◽
pp. 43-59
◽
Keyword(s):
2020 ◽
Vol 72
(1)
◽
pp. 155-170
◽
Keyword(s):
2009 ◽
Vol 50
(11-12)
◽
pp. 1553-1570
◽
Keyword(s):