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arXiv · 1911.10881

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

Oscar Agudelo·Michal Kowalczyk·Matteo Rizzi
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Abstract

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 diverge logarithmically from the Lawson cone at infinity. The construction is based on a careful study of the Jacobi-Toda system on a given $O(m)\times O(n)$-invariant manifold, which is asymptotic to the Lawson cone at infinity.

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Oscar Agudelo, Michal Kowalczyk, Matteo Rizzi. 2020-09-29. Doubling construction for $O(m)\times O(n)$-invariant solutions to the Allen-Cahn equation. https://arxiv.org/abs/1911.10881

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