### 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 | |

State | Published - Jan 1 1991 |

Externally published | Yes |

### Fingerprint

### 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

### Cite this

**Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium.** / Robinson, Sam L.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 32, no. 3, pp. 651-655. https://doi.org/10.1063/1.529407

}

TY - JOUR

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

AU - Robinson, Sam L

PY - 1991/1/1

Y1 - 1991/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=0040871354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040871354&partnerID=8YFLogxK

U2 - 10.1063/1.529407

DO - 10.1063/1.529407

M3 - Article

VL - 32

SP - 651

EP - 655

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

ER -