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Artículo de publicación ISIIn this paper, we construct a wealth of bounded, entire solutions of the Allen–Cahnequation in the plane. The asymptotic behavior at infinity of these solutions is determinedby 2L half affine lines, in the sense that, along each of these half affine lines, the solutionis close to a suitable translated and rotated copy of a one dimensional heteroclinic solution.The solutions we construct belong to a smooth 2L-dimensional family of bounded, entiresolutions of the Allen–Cahn equation, in agreement with the result of del Pino (Trans AmMath Soc 365(2):721–766, 2010) and, in some sense, they provide a description of a collarneighborhood of part of the compactification of the moduli space of 2L-ended solutions forthe Allen–Cahn equation. Our construction is inspired by a construction of minimal surfacesby Traizet.NSFC, SRF for ROCS, SEM, Chilean research grants Fondecyt, Fondo Basal CMM-Chile, Project Anillo, MathAmSud project NAPDE, General Research Fund from RGC of Hong Kon

End-to-end construction for the Allen–Cahn equation in the plane