Green's function for the lossy wave equation

• Main Authors: R. Aleixo, E. Capelas de Oliveira
• Format: Article
• Language: Portuguese
• Published: Sociedade Brasileira de Física
• Series: Revista Brasileira de Ensino de Física
• Subjects: sonine-bessel; representação integral; equação da onda dissipativa
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172008000100003&lng=en&tlng=en

Using an integral representation for the first kind Hankel (Hankel-Bessel Integral Representation) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function. Using the Sonine-Bessel integral representation we obtain the Fourier cosine integral transform of the zero order Bessel function. As an application we present the calculation of the Green's function associated with a second-order partial differential equation, particularly a wave equation for a lossy two-dimensional medium. This application is associated with the transient electromagnetic field radiated by a pulsed source in the presence of dispersive media, which is of great importance in the theory of geophysical prospecting, lightning studies and development of pulsed antenna systems.