BIRS Workshop Lecture Videos
New multiple end solutions in the Allen-Cahn and the generalized second PainlevÃ Â¨ equation. Kowalczyk, Michal
In this talk I will discuss two new constructions of the multiple end solutions. In the case of the Allen-Cahn equation the ends are asymptotic to the Simons cone in $\mathbb R^8$. The case of the generalized second Painlev\'e equation in $\mathbb R^2$ is somehow different since there is no apparent underlying geometric problem. Yet we can interpret the behavior of the solution as being asymptotic along the axis to: two one dimensional Hastings-McLeod solution, the heteroclinic solution of the Allen-Cahn equation and the trivial solution.
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