On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions

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Concentration on curves for nonlinear Schrödinger Equations (2007, background): “In [1, 20, 19, 33] related singular perturbation problems involving the”
MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2 (2010, methodology): “For example, solutions concentrating along non-degenerate, minimal hypersurfaces of a compact manifold were found in [28] (see also [ 22 ]).”
From Constant mean Curvature Hypersurfaces to the Gradient Theory of Phase Transitions (2003, result): “0) there exists uε, critical point of u−→ Eε(u), such that uε converges uniformly to 1 on compacts subsets of M+(N) (resp. to −1 on compacts subsets of M−(N)). Let us mention the work of M. Kowalczyk [13] where a similar result is obtained when Mis a two dimensional domain of R2 and Nis a line segme”
The Toda System and Clustering Interfaces in the Allen–Cahn equation (2008, background): “In [24] the second author has established that if (1.”