UNSPECIFIED. (1997) Stability of the two- and three-dimensional kink solutions to the Cahn-Hilliard equation. PHYSICAL REVIEW E, 55 (5 Part A). pp. 5427-5432. ISSN 1063-651X

Abstract

We give an analysis of the Cahn-Hilliard equation, which admits both cylindrically and spherically symmetric, stationary kink solutions. Since analytic expressions for these solutions are unobtainable in closed form, we devise an approximate method of solution taking the radius as large and scaling variables in its reciprocal. To lowest order, the solution is that of the one-dimensional kink solution which has been analyzed in earlier work. In this paper we begin by investigating the stability of the cylindrically symmetric kink solution to small perturbations involving angular and z dependence. It is found that the solution is stable to perturbations involving angular variation, but is unstable to a general perturbation. We go on to show that the spherically symmetric kink solution is stable to all small perturbations.

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