# Dynamics of wave propagation and curvature of discriminants

Annales de l'institut Fourier (2000)

- Volume: 50, Issue: 6, page 1945-1981
- ISSN: 0373-0956

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topPalamodov, Victor P.. "Dynamics of wave propagation and curvature of discriminants." Annales de l'institut Fourier 50.6 (2000): 1945-1981. <http://eudml.org/doc/75475>.

@article{Palamodov2000,

abstract = {For a Lagrange distribution of order zero we consider a quadratic integral which has logarithmic divergence at the singular locus of the distribution. The residue of the asymptotics is a Hermitian form evaluated in the space of positive distributions supported in the locus. An asymptotic analysis of the residue density is given in terms of the curvature form of the locus. We state a conservation law for the residue of the impulse-energy tensor of solutions of the wave equation which extends the classical conservation law in the geometrical optics.},

author = {Palamodov, Victor P.},

journal = {Annales de l'institut Fourier},

keywords = {Fourier integral; Lagrange manifold; contact bundle; symbol; discriminant; residue; curvature; conservation law},

language = {eng},

number = {6},

pages = {1945-1981},

publisher = {Association des Annales de l'Institut Fourier},

title = {Dynamics of wave propagation and curvature of discriminants},

url = {http://eudml.org/doc/75475},

volume = {50},

year = {2000},

}

TY - JOUR

AU - Palamodov, Victor P.

TI - Dynamics of wave propagation and curvature of discriminants

JO - Annales de l'institut Fourier

PY - 2000

PB - Association des Annales de l'Institut Fourier

VL - 50

IS - 6

SP - 1945

EP - 1981

AB - For a Lagrange distribution of order zero we consider a quadratic integral which has logarithmic divergence at the singular locus of the distribution. The residue of the asymptotics is a Hermitian form evaluated in the space of positive distributions supported in the locus. An asymptotic analysis of the residue density is given in terms of the curvature form of the locus. We state a conservation law for the residue of the impulse-energy tensor of solutions of the wave equation which extends the classical conservation law in the geometrical optics.

LA - eng

KW - Fourier integral; Lagrange manifold; contact bundle; symbol; discriminant; residue; curvature; conservation law

UR - http://eudml.org/doc/75475

ER -

## References

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- [2] J.J. DUISTERMAAT, Fourier Integral Operators, Birkhäuser, 1996. Zbl0841.35137MR96m:58245
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- [5] L. HÖRMANDER, Fourier integral operators, I, Acta Math., 127, 1-2 (1971), 79-183. Zbl0212.46601MR52 #9299
- [6] L. HÖRMANDER, The Analysis of Linear Partial Differential Operators, IV, Fourier Integral Operators, Springer, 1985. Zbl0601.35001
- [7] E. LOOIJENGA, The complement to the bifurcation variety of a simple singularity, Invent. Math., 23 (1974), 105-116. Zbl0278.32008
- [8] B. MALGRANGE, Ideals of differentiable functions, Oxford University Press, 1966. Zbl0177.17902
- [9] V.P. PALAMODOV, Distributions and Harmonic Analysis, Encyclopaedia of Mathematical Science, 72, Springer, 1993, 1-127. Zbl0826.46025MR1447631
- [10] L. SCHWARTZ, Théorie des distributions, Hermann, 1966. Zbl0149.09501
- [11] J.-C. TOUGERON, Idéaux de fonctions différentiables, Ann. Inst. Fourier, 18-1 (1968), 177-240. Zbl0188.45102MR39 #2171

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