International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 6, Pages 371-381

Wave splitting for first-order systems of equations

G. Caviglia1 and A. Morro2

1Department of Mathematics, DIMA, University of Genoa, Via Dodecaneso 35, Genoa 16146, Italy
2Biophysical and Electronic Engineering Department, DIBE, University of Genoa, Via Opera Pia 11a, Genoa 16145, Italy

Received 23 October 2001

Copyright © 2002 G. Caviglia and A. Morro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Systems of first-order partial differential equations are considered and the possible decomposition of the solutions in forward and backward propagating is investigated. After a review of a customary procedure in the space-time domain (wave splitting), attention is addressed to systems in the Fourier-transform domain, thus considering frequency-dependent functions of the space variable. The characterization is given for the direction of propagation and applications are developed to some cases of physical interest.