Doubling construction for $O(m)\times O(n)$-invariant solutions to the Allen-Cahn equation

Oscar Agudelo, Michal Kowalczyk, Matteo Rizzi

We construct new families of two-ended $O(m)\times O(n)$-invariant solutions to the Allen- Cahn equation Δu+u-u3=0 in ${\mathbb{R}}^{N+1}$, with $N\ge 7$, whose zero level sets diver…