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In this paper, we prove even symmetry and monotonicity of certain solutionsof 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 withrespect to two orthogonal axes. A classification scheme of general entiresolutions with {\it finite Morse index} is also presented using energyquantization.

Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two Dimensions