Higher order periodic solutions of coupled ϕ4 and ϕ6 models

Abstract

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 Lamé 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.