Higher order periodic solutions of coupled φ4 and φ6 models

We obtain several higher order periodic solutions of (i) a coupled symmetric φ4 model in an external field, (ii) a coupled asymmetric φ4 model, (iii) a coupled symmetric-asymmetric φ4 model and (iv) a coupled φ6 model in terms of Lame polynomials and obtain the corresponding hyperbolic solutions in the appropriate limit. All 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. Possible physical applications of these solutions include periodic domain walls in magnetic and structural phase transitions as well as in field theory.