How to slove this coupled BVP equation

Here is the coupled equation

u1'' = u1 + u1^3 - 2* u1u2-(1/r)u1'
u2'' = u2 -2u2^3 + u2^3-(1/r)u2'- (u1*u1)
with this condition
u1(0)=0, u1'(\infinite)=0
u2'(0)=0,u2'(\infinite)=0 (The mixed boundary condition)

from dolfin import *

# Number of elements
nel = 30

# Polynomial order
p = 2

# Create mesh and function space
mesh = IntervalMesh(nel,0,1)

V = FunctionSpace(mesh,"CG",p)

# Product space 
V2 = V*V

# Define boundary values 
boundary= Expression("x[0]")

def u0_boundary(x,on_boundary):
    return on_boundary

# Dirichlet boundary conditions
bc = DirichletBC(V2.sub(0),boundary,u0_boundary)
bcs = [bc,0]

# Define variational problem
(u1,u2) = TrialFunctions(V2)
(v1,v2) = TestFunctions(V2)

f1 = Expression("-u1-u1*u1*u1+2*u1*u2")
f2 = Expression("-u2+2*u2*u2-u2*u2*u2+u1*u1")
g  = Expression("pow(x[0],-1)")
a = inner(grad(u1),grad(v1))*dx + g*grad(u1)*v1*dx + \
    g*grad(u2)*v2*dx + inner(grad(u2),grad(v2))*dx

L = f1*v1*dx + f2*v2*dx + v1*ds +v2*ds

u = Function(V2)
solve(a == L, u, bcs)

u1,u2 = u.split()
plot(u1,title="u_1")
plot(u2,title="u_2")
interactive()