We treat the stability index for traveling-wave solutions of one-dimensional reaction-diffusion equations due to Alexander, Gardner, and Jones [J. Reine Angew. Math., 410 (1990), pp. 167--212]. An extension of the stability index which makes the index robust to perturbation is given and, using the extension, an additive formula for a gluing bifurcation of traveling waves is proven. Wealso consider certain heteroclinic bifurcations as an application, some specific examples of which are discussed.
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Shunsaku Nii (1997) studied this question.
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