Multiple Internal Layer Solutions Generated by Spatially Oscillatory Perturbations,

For a singularly perturbed system of reaction-diffusion equations, we study the bifurcation of internal layer solutions due to the addition of a spatially oscillatory term. In the singular limit, the existence and stability of internal layer solutions are determined by the intersection of afast jump surfaceΓ1and aslow switching curve . The case when the intersection is transverse was studied by X.-B. Lin (Construction and asymptotic stability of structurally stable internal layer solutions, preprint). In this paper, we show that whenΓ1intersects with tangentially, saddle-node or cusp type bifurcation may occur. Higher order expansions of internal layer solutions and eigenvalue–eigenfunctions are also presented. To find a true internal layer solution and true eigenvalue-eigenfunctions, we use a Newtonʹs method in functions spaces that is suitable for numerical computations.