Multiple end solutions to the Allen-Cahn equation in
Michał Kowalczyk, Yong Liu, Frank Pacard (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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An entire solution of the Allen-Cahn equation , where is an odd function and has exactly three zeros at and , e.g. , is called a end solution if its nodal set is asymptotic to half lines, and if along each of these half lines the function looks (up to a multiplication by ) like the one dimensional, odd, heteroclinic solution , of . In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space...