The stability of homoclinic pulses: a generalisation of Evans's method

Abstract Evans's method provides a stability analysis for pulse-like solutions of partial differential equations which is particularly well suited to numerical implementation. The original formulation was only applicable to pulses corresponding to orbits homoclinic to a fixed point with an unstable manifold of dimension exactly one. This paper extends the method of Evans by removing this restriction on the dimension of the unstable manifold. I also show how to apply the method to heteroclinic orbits.