Higher Order Periodic Solutions of Coupled phi4 Models

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.