[Authors]
 M. V. Perel and M. S. Sidorenko
	
[Title]
 Wavelet analysis in solving the Cauchy problem for the wave equation
 in three dimensional space

[AMS Subj-class]
 35L05 Wave equation
 42C40 Wavelets
 35E15 Initial value problems

[Abstract]
 We propose a new method of solving the Cauchy problem for the wave
 equation in three-dimensional space. The method is based on continuous
 wavelet-analysis. We show that the exact non-stationary solution of
 the wave equation with finite energy found in [A.P. Kiselev, M.V. Perel:
 J. Math. Phys., 4, 41 (2000)] at any fixed moment of time should be
 regarded as a mother wavelet. It is a new three-dimensional axially
 symmetric wavelet which is given by a simple explicit formula as well
 as its Fourier transform. This wavelet has an infinite number of
 vanishing moments. We show that using the wavelet decomposition of the
 initial data we can find the exact formula for the solution of the Cauchy
 problem as a linear superposition of "Gaussian packets".

[Keywords]
 wave equation, wavelet, initial value problem

[Comments]
 LaTeX, English, 5 pp.
 The paper is submitted to the Sixth International Conference on
 Mathematical and Numerical Aspects of Wave Propagation
 Jyvaskyla,  Finland,  June 30 - July 4, 2003

[Contact e-mail]
 perel@mph.phys.spbu.ru