Generalization of Bateman–Hillion progressive wave and Bessel–Gauss pulse solutions of the wave equation via a separation of variables
Aleksei P Kiselev; Aleksei P Kiselev; St Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St Petersburg 191011, Russia; Laboratoire de Mécanique Physique, Université Bordeaux 1, 351 Cours Libération, 33405 Talence, France
Журнал:
Journal of Physics A: Mathematical and General
Дата:
2003-06-13
Аннотация:
Two new families of exact solutions of the wave equation u<sub>xx</sub> + u<sub>yy</sub> + u<sub>zz</sub> − c<sup>−2</sup>u<sub>tt</sub> 0 generalizing Bessel–Gauss pulses and Bateman–Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables.
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