Abstract

In this paper we study rotationally symmetric solutions of the Cahn-Hilliard equation in R-3 constructed in [13] by the authors. These solutions form a one-parameter family analog to the family of the Delaunay surfaces, and in fact the zero level sets of their blowdowns approach these surfaces. Presently, we go a step further and show that their stability properties are inherited from the stability properties of the Delaunay surfaces. Our main result states that the rotationally symmetric solutions are non degenerate and that they have exactly six Jacobi fields of temperate growth coming from the natural invariances of the problem (three translations and two rotations) and the variation of the Delaunay parameter.