Wolfgang says:
> Actually, the original system can be further reduced to a system of
> the form....
> x^4-2*a*x^2+x+a^2-b=0
These nice transformations do leave us with a neater quartic, but isn't
the solution of that quartic still a mess? It doesn't seem to give any
good qualitative feel for the solution. That is why I looked at A<<1.
James, give us some guidance here. What are you looking for? A
qualitative characterization of the solutions? A fast way of
calculating solutions for particular parameter values? What are the
interesting ranges of the parameters? Which are the interesting
solutions? -- presumably only the ones with Bmin<B<Bmax and Fmin<F<Fmax,
but in your example, one solution is near Bmin, two are near Bmax, and
one is in between. Are these all interesting solutions?
-s