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Existence and stability of asymptotically oscillatory triple pulses

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Abstract

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.

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Authors and Affiliations

  1. Dept of Mathematics, University of Maryland, 20742, College Park, Maryland

    J. C. Alexander

  2. Div. of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    C. K. R. T. Jones

Authors
  1. J. C. Alexander
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  2. C. K. R. T. Jones
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Additional information

Dedicated with great respect to Klaus Kirchgässner on the occasion of his 60th birthday

Research 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.

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Alexander, J.C., Jones, C.K.R.T. Existence and stability of asymptotically oscillatory triple pulses. Z. angew. Math. Phys. 44, 189–200 (1993). https://doi.org/10.1007/BF00914281

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  • DOI: https://doi.org/10.1007/BF00914281

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