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 spati ally oscillatory term. In the singular limit, the existence and stability o f internal layer solutions are determined by the intersection of a fast jum p surface Gamma(1) and a slow switching curve C The case when the intersect ion is transverse was studied by X.-B. Lin (Construction and asymptotic sta bility of structurally stable internal layer solutions, preprint). In this paper, we show that when Gamma(1) intersects with C tangentially, saddle-no de 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 Newton's method in functions spaces that is suitable for numerical computat ions. (C) 1999 Academic Press.