Domain Wall and Periodic Solutions of Coupled Asymmetric Double Well Models

Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of such a coupled asymmetric model in terms of elliptic functions (domain wall arrays) and obtain single domain wall solutions in specific limits. We also calculate the energy and interaction between solitons for various solutions. Both topological (kink-like at $T=T_c$) and nontopological (pulse-like for $T\ne T_c$) domain wall solutions are obtained. We relate some of these solutions to domain walls in hydrogen bonded materials and also in the field theory context. As a byproduct, we also obtain a new one parameter family of kink solutions of the uncoupled asymmetric double well model.