Existence and stability of asymptotically oscillatory triple pulses

Triple pulses are constructed for systems of two coupled reaction-diffusion equations with an asymptotically oscillatory single pulse. In (Alexander and Jones 1993]) it has been shown that an infinite sequence of double pulses can be constructed near the single pulse. Under the condition that the wave speed of a stable double pulse coincides with that of the single pulse, it is shown here that an infinite sequence of triple pulses can be constructed. These pulses have the form of the double pulse concatenated with a further single pulse far behind, and cannot be constructed in the same way for the situations considered by previous authors. Moreover, the pulses are shown to be alternately stable and unstable.Dedicated with great respect to Klaus Kirchgässner on the occasion of his 60th birthdayResearch partially supported by the National Science Foundation under grant DMS-90-01788.Research partially supported by the National Science Foundation under grant DMS-91-00085.