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We study heteroclinic solutions of a generalized Frenkel-Kontorova model.Using the methods of Rabinowitz and Stredulinsky, we prove that if the rotationvector of the configuration is rational and if there is an adjacent pair ofperiodic configurations, then there is a solution that is heteroclinic in onefixed direction and periodic in other directions. Furthermore, if the aboveheteroclinic solutions have an adjacent pair, then there is a solution that isheteroclinic in two directions and periodic in other directions. The procedurecan be repeated to produce more complex solutions. Thus we obtain a variationalconstruction for these minimal and Birkhoff solutions.

Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and Stredulinsky