  We consider a class of semilinear elliptic system of the form $-\Delta
u(x,y)+\nabla W(u(x,y))=0,\quad (x,y)\in\R^{2}$ 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 $-\ddot q(x)+\nabla
W(q(x))=0,\ x\in\R$, which connect the two minima of $W$ as $x\to\pm\infty$ has
a discrete structure, then the given system has infinitely many layered
solutions.
