MULTIPLE-LAYER SOLUTIONS TO THE ALLEN-CAHN EQUATION ON HYPERBOLIC SPACE.

In this paper we study the existence of multiple-layer solutions to the elliptic Allen-Cahn equation in hyperbolic space: ... here F is a nonnegative double-well potential with nondegenerate minima. We prove that for any collection of widely separated, nonintersecting hyperplanes in Hn, there is a solution to this equation which has a nodal set very close to this collection of hyperplanes. Unlike the corresponding problem in Rn, there are no constraints beyond the separation parameter. [ABSTRACT FROM AUTHOR]