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We consider the travelling wave that represents the simultaneous propagation of a voltage pulse along the length of two coupled nerve fibers. Conditions are given which guarantee the existence and stability of the wave. Two advances in the geometric techniques in the stability analysis of travelling waves are given: the first involves the Maslov Index, and the other the Exchange Lemma.doi:10.1512/iumj.1995.44.1984 fatcat:jl2fdy3srbcabkvr7xqy42stmm