Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium

Sam L. Robinson

doi:10.1063/1.529407

Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium

Sam L. Robinson

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

An explicit integral representation is obtained in the 0 limit of the solution of the wave equation utt=c(x)2u on Rn(n3) with initial data of the form u(x,0)=f(x)eiS(x)/. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by timedependent geometrical optics.

Original language	English (US)
Pages (from-to)	651-655
Number of pages	5
Journal	Journal of Mathematical Physics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1063/1.529407
State	Published - Mar 1991
Externally published	Yes

Keywords

ASYMPTOTIC SOLUTIONS
FREQUENCY DEPENDENCE
GAUSS FUNCTION
GEOMETRICAL OPTICS
INHOMOGENEOUS MATERIALS
INTEGRALS
PULSES
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
TIME DEPENDENCE
WAVE EQUATIONS

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.529407

Cite this

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title = "Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium",

abstract = "An explicit integral representation is obtained in the 0 limit of the solution of the wave equation utt=c(x)2u on Rn(n3) with initial data of the form u(x,0)=f(x)eiS(x)/. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by timedependent geometrical optics.",

keywords = "ASYMPTOTIC SOLUTIONS, FREQUENCY DEPENDENCE, GAUSS FUNCTION, GEOMETRICAL OPTICS, INHOMOGENEOUS MATERIALS, INTEGRALS, PULSES, QUANTUM MECHANICS, SEMICLASSICAL APPROXIMATION, TIME DEPENDENCE, WAVE EQUATIONS",

author = "Robinson, {Sam L.}",

year = "1991",

month = mar,

doi = "10.1063/1.529407",

language = "English (US)",

volume = "32",

pages = "651--655",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

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T1 - Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium

AU - Robinson, Sam L.

PY - 1991/3

Y1 - 1991/3

N2 - An explicit integral representation is obtained in the 0 limit of the solution of the wave equation utt=c(x)2u on Rn(n3) with initial data of the form u(x,0)=f(x)eiS(x)/. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by timedependent geometrical optics.

AB - An explicit integral representation is obtained in the 0 limit of the solution of the wave equation utt=c(x)2u on Rn(n3) with initial data of the form u(x,0)=f(x)eiS(x)/. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by timedependent geometrical optics.

KW - ASYMPTOTIC SOLUTIONS

KW - FREQUENCY DEPENDENCE

KW - GAUSS FUNCTION

KW - GEOMETRICAL OPTICS

KW - INHOMOGENEOUS MATERIALS

KW - INTEGRALS

KW - PULSES

KW - QUANTUM MECHANICS

KW - SEMICLASSICAL APPROXIMATION

KW - TIME DEPENDENCE

KW - WAVE EQUATIONS

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U2 - 10.1063/1.529407

DO - 10.1063/1.529407

M3 - Article

AN - SCOPUS:0040871354

SN - 0022-2488

VL - 32

SP - 651

EP - 655

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

ER -

Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium

Abstract

Keywords

ASJC Scopus subject areas

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