Wave
Packet Propagation
In many fields transmission of information from one x,t space-time region to another involves a source of excitation in one region, propagation of the excitation through a medium, and calculation of the response in another region. The space-time dependent source may have an arbitrary configuration, for example as a u(x,t) function representative of a wave packet, i.e. a superposition of elementary oscillatory waveforms. The space-time dependent medium may be homogeneous or non-homogeneous. The IGL program provides an efficient method of calculation of the space-time structure of the response to a prescribed source.
Many wave packet propagation problems arise in analyses of physical fields and are described mathematically by partial differential wave equations. Their solution usually requires a balanced mix of analytical and numerical techniques and an appropriate choice of mathematical representation. In the following we contrast the relative ease of solution of a class of wave propagation problems by viewing them in different representations, with the intent of enhancing conceptual insights into the basic processes underlying the different representations:
Fourier Transform (k,t) Space,
Wigner Transform (k,x,t) Phase Space