The classification of four end solutions of the Allen-Cahn equation on the plane

Frank Pacard, Michal Kowalczyk, Yong Liu

An entire solution of the Allen-Cahn equation $\Delta u=f(u)$, where $f$ has exactly three zeros at $\pm 1$ and 0, is balanced and odd, e.g. $f(u)=u(u^2-1)$, is called a $2k$-ended solut…