Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two   Dimensions
  In this paper, we prove even symmetry and monotonicity of certain solutions of Allen-Cahn equation in a half plane. We also show that entire solutions with {\it finite Morse index} and {\it four ends} must be evenly symmetric with respect to two orthogonal axes. A classification scheme of general entire solutions with {\it finite Morse index} is also presented using energy quantization. 
Changfeng Gui
math.AP