Doubling construction for O(m)×O(n) invariant solutions to the Allen–Cahn equation. (March 2022) - Agudelo, Oscar; Kowalczyk, Michał; Rizzi, Matteo
Abstract: We construct new families of two-ended O ( m ) × O ( n ) -invariant solutions to the Allen–Cahn equation Δ u + u − u 3 =0 in R N + 1, with N ≥ 7, whose zero level sets diverge logarithmically from the Lawson cone at infinity. The construction is based on a careful study of the Jacobi–Toda system on a given O ( m ) × O ( n ) -invariant manifold, which is asymptotic to the Lawson cone at infinity.