Periodic and heteroclinic type solutions for systems of Allen-Cahn equations

We consider a class of semilinear elliptic system of the form $-\Delta u(x,y)+\nabla W(u(x,y))=0$ on $\R^2$, where $W:\R^2\to\R$ is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions to the one dimensional system which connect the two minima of $W$ as $x\to\pm\infty$ has a discrete structure, then the two dimensional system has infinitely many layered solutions with prescribed energy.