Is there analitical solution of the problem?

The nonlinear equations are very impotant in many areas of physics,
but the exact analitycal solutions are known only for some equations
of specific form. Recently I've come across the following problem.
imagin you have the liquid near critical point, the behavior of such
fluid is determined by so called Ginzburg-Landau equation. It may be
written in the next form (TeX notations)

-\triangle \rho +(\rho-\rho_1)(\rho-\rho_2)(\rho-(rho_1+rho_2)/2)=0

here \rho_1 and \rho_2 are the constants (the liquid and gase phase
densities). I need the analitycal solution of this problem in the case
of spherical symmetry and under the following boundary conditions
\rho(R)=0, R<\infty
\rho(\infty)=\rho_2
The sollution corresponds to the bubble dissolved in water.
I admit that there is no such solution but the equation is very simple
and it should be in my opinion. Suppose there is no one then if the solution of
the problem exists when \rho_1=0
or in other words
-\frac{d^2 \rho}{dr^2}-\frac{2}{r} \frac{d\rho}{dr}+\rho (\rho-\rho_2)
(\rho-\rho_2/2)=0
\rho(R)=0
\rho(\infty)=\rho_2
Ideed I don't need the strict derivation of the solution, It would be enough to know if there is one and may be how to find it in some words.
Thank you.
George