Entire solutions in R2 for a class of Allen-Cahn equations

We consider a class of semilinear elliptic equations of the form -epsilon(2)Delta u(x, y) + a(x)W' (u(x, y)) = 0, (x, y) is an element of R-2 where epsilon > 0, a : R -> R is a periodic, positive function and W : R -> R is modeled on the classical two well Ginzburg-Landau potential W(s) = (s(2) - 1)(2). We look for solutions to (0.1) which verify the asymptotic conditions u(x, y) -> +/- 1 as x -> +/-infinity uniformly with respect to y. R. We show via variational methods that if epsilon is sufficiently small and a is not constant, then (0.1) admits infinitely many of such solutions, distinct up to translations, which do not exhibit one dimensional symmetries.