Let Σ be a surface of constant mean curvature in R3 with multiple Delaunay ends. Assuming that is non degenerate this paper we construct new solutions to the Cahn-Hilliard equation εΔu+ε−1u(1−u2)=ℓε such as ε→0 zero level set uε approaches Σ. Moreover, on compacts connected components R3∖Σ have 1−|uε|→0 uniformly.