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We obtain geometric insight into the stability of traveling pulses forreaction-diffusion equations with skew-gradient structure. For such systems, aMaslov index of the traveling wave can be defined and related to the eigenvalueequation for the linearization $L$ about the wave. We prove two main resultsabout this index. First, for general skew-gradient systems, it is shown thatthe Maslov index gives a lower bound on the number of real, unstableeigenvalues of $L$. Second, we show how the Maslov index gives an exact countof all unstable eigenvalues for fast traveling waves in a FitzHugh-Nagumosystem. The latter proof involves the Evans function and reveals a newgeometric way of understanding algebraic multiplicity of eigenvalues.

Opening the Maslov Box for Traveling Waves in Skew-Gradient Systems