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The spectral problem associated with the linearization about solitary wavesof spinor systems or optical coupled mode equations supporting gap solitons isformulated in terms of the Evans function, a complex analytic function whosezeros correspond to eigenvalues. These problems may exhibit oscillatoryinstabilities where eigenvalues detach from the edges of the continuousspectrum, so called edge bifurcations. A numerical framework, based on a fastrobust shooting algorithm using exterior algebra is described. The completealgorithm is robust in the sense that it does not produce spurious unstableeigenvalues. The algorithm allows to locate exactly where the unstable discreteeigenvalues detach from the continuous spectrum. Moreover, the algorithm allowsfor stable shooting along multi-dimensional stable and unstable manifolds. Themethod is illustrated by computing the stability and instability of gapsolitary waves of a coupled mode model.Comment: key words: gap solitary wave, numerical Evans function, edge  bifurcation, exterior algebra, oscillatory instability, massive Thirring  model. accepted for publication in SIAD

A Robust Numerical Method to Study Oscillatory Instability of Gap Solitary Waves