I have just learnt that accelerating charges produce electromagnetic radiation. When a charge initially at rest suddenly accelerates, the transition between the new and old elctric field lines propagates out as a wave at the speed of light. Moreover, the electric field is transverse to the direction of propagation. This phenomenon is explained here: http://www.springer.com/cda/content/document/cda_downloaddocument/9783642309694-c1.pdf?SGWID=0-0-45-1349311-p174514828
However, it doesn't seem to look like a harmonic(sine) wave to me. So if it doesn't have oscillating electric and magnetic fields, how is it classified as an electromagnetic wave? Also, does it satisfy the wave equation? For something to be called an electromagnetic wave, do we need to have sinusoidal oscillations of electric and magnetic fields?
One more question:Are all the electromagnetic waves that we observe in the universe sinusoidal? Or are there other types as well?
Thanks in advance.