tsunamiBTP

I have rather nasty vector partial diff eq which I think has been addressed before; however, when I vistied a few websites to classify the equation the notation of these websites is not necessarily what I am accustomed to. I have attached the equation here & was wondering if anyone could point me in the right direction so I can see how others approached solving the problem. I suspect this has applications in electromagnetism, but it may be applicable elsewhere, MAYBE gas dynamics? I have a solution but would like to compare mine with others. Appreciate any feedback eq of choice.pdf

I have attached a pdf of output from MAPLE attempting to evaluate an integral of an exponential function containing a complex irrational trig function as the exponent. MAPLE could not evaluate it when integrating with respect to the hangle phi. I then transformed the integral via varible substitutions to hopefully get it in a form that might be executable, but no luck there either. Any suggestions? This integral is a portion of a solution of a radiation wave emanating in the vicinity of source that is configured as a disc. integral output.pdf