The second Painlevé O.D.E. y00 - xy - 2y3 = 0, x 2 R, is known to play an important role in the theory of integrable systems, random matrices, Bose-Einstein condensates and other problems. The generalized second Painlevé equation Δy -x1 y -2y3 = 0, (x1, x2) 2 R2, is obtained by multiplying by -x1 the linear term u of the Allen-Cahn equation Δ= u3 - u. It involves a non autonomous potential H(x1, y) which is bistable for every fixed x1 < 0, and thus describes as the Allen-Cahn equation a phase transition model. The scope of this paper is to construct a solution y connecting along the vertical direction x2, the two branches of minima of H parametrized by x1. This solution plays a similar role that the heteroclinic orbit for the Allen-Cahn equation. It is the the first to our knowledge solution of the Painlevé P.D.E. both relevant from the applications point of view (liquid crystals), and mathematically interesting.