I have a nonlinear partial diff eq which I am sure has been categorized.  How do I go about finding literature on the eq & the approach to solve it.  I have visited various websites that have catalogs of nonlinear partial diff eq's.  The problem is notation is so NONSTANDARD I have no IDEA what I am reading.  I have included a PDF eq_of_choice.pdf with my notation which I am familiar with. ...

Included below is vector partial diff eq I am working with.  To get rid of the time deriv's I took the LaPlace transform & the remaining spatial eq in the s-domain is listed.  To make matters simpler I set beta = 0 to get rid of the curl of the field.  What remains is essentially the Helmholtz eq.  To simplify further I just found the homogeneous soln for the x direction only.

As can be seen the eigenfunctions are exponentials with s beneath...

Not sure why pdsolve is choking on my input.  The file is attached below.  It works fine for my first expression if the term without the square root sign is not included.  When I include that term as you will see at the end it simply does nothing?

Any advice??

I was successful @ splitting the coupled eq into the 3 constituent PDE's but have been unsuccessful to get MAPLE to generate the characteristic solutions except for the 1st one for X which is the basic solution to the Helmholtz eq.

Can someone with more savy with MAPLE verify whar I have so far & advise me how to proceed to solve for Y & Z?  I have uploaded my file.  My expereince with MAPLE vector calc package is limited.

appreciate the assistance

I am working with a 3 dimensional vector partial diff eq that resembles the Helmholtz equation, but there is a curl of the vecotr field as the middle term.

ie-->LaPlacian(F)+2beta*gamma^2*curl(F)+gamma^2*F = 0

Anyone have knowledge or references for me to look over to solve this equation?