  In this work we construct a family of entire bounded solution for the
singulary perturbed Inhomogeneous Allen-Cahn Equation
$\ep^2\div\left(a(x)\nabla u\right)-a(x)F'(u)=0$ in $\R^2$, where $\ep\to 0$.
The nodal set of these solutions is close to a "nondegenerate" curve which is
asymptotically two non paralell straight lines. Here $F'$ is a double-well
potential and $a$ is a smooth positive function. We also provide example of
curves and functions $a$ where our result applies. This work is in connection
with the results found by Z.Du and B.Lai, Z.Du and C.Gui, and F. Pacard and M.
Ritore, in "Transition layers for an inhomogeneus Allen-Cahn equation in
Riemannian Manifolds", "Interior layers for an inhomogeneous Allen-Cahn
equation", "From the constant mean curvature hypersurfaces to the gradient
theory of phase transitions" respectively, where they handle the compact case.
