  We obtain several higher order exact periodic solutions of (i) a coupled
symmetric phi4 model in an external field, (ii) an asymmetric coupled phi4
model, (iii) an asymmetric-symmetric coupled phi4 model, in terms of Lame
polynomials of order two and obtain the corresponding hyperbolic solutions in
the appropriate limit. These solutions are unusual in the sense that while they
are the solutions of the coupled problems, they are not the solutions of the
corresponding uncoupled problems.
