🚀 go-pugleaf

Please, I need help---by way of even merely a suggestion as to what
"canned" FORTRAN or Mathematica software packages to use for numerical
integration---in solving the following system of nonlinear partial
differential equations. (Laplace transforms work nicely on systems like
this when they are linear. But this system is certainly not linear!)

(The following details are provided to show what *kind* of system of
differential equations are under consideration. For example, as far
as BOUNDARY CONDITIONS are concerned at *one* of the two boundary
points, the actual *values* of the functions or of their first partial
derivatives with respect to x are *not* given, just relations among
them at the point in question!)

Given that

     U = U(x,t)
     V = V(x,t)
     W = W(x,t)

and that "dot" and "prime" represent partial differentiation
with respect t and x, respectively,
     .
     U = a U'' + b U W + c V^2

     .
     V = A V'' - b U W - c V^2

     .
     W = B W'' + b U W + c V^2 + C W

where a, b, c, A, B, and C are constants,
subject to the

BOUNDARY CONDITIONS:

(1) at x = 0, t > 0:

     U' = - V' = W',
     i.e. U' + V' = 0 and V' + W' = 0
     and
     U/V = V/W = f(t) [i.e. a given function of t]

(2) at x = "infinity," t > 0:

     U = a given constant, <--------
     V = W = 0,                     |
                                    |
 and to the                         |
                                    |
INITIAL CONDITIONS:                 |
                                    |
(3) at t = 0, x > 0:                |
                                    |
     U = the same given constant ---
     V = W = 0

How, please, might this system of partial differential equations be
solved, presumably or hopefully using Laplace transforms, "canned"
FORTRAN subroutines (e.g. IMSL), Mathematica, MACSYMA, or whatever?

Surely I don't expect anyone to actually solve them, but *suggestions*
would be very much appreciated!

Thanks!!

Carey Briggs