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Asymptotic expansion of the wobbling kink

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Abstract

We use the method of multiple scales to study the wobbling kink of the ϕ4 equation. We show that the amplitude of the wobbling decays very slowly, proportionally to t−1/2, and the wobbler hence turns out to be an extremely long-lived object.

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Authors and Affiliations

  1. CSIR Computational Aerodynamics, Pretoria, South Africa

    O. F. Oxtoby

  2. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa

    I. V. Barashenkov

Authors
  1. O. F. Oxtoby
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  2. I. V. Barashenkov
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Correspondence to O. F. Oxtoby.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 527–535, June, 2009.

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Oxtoby, O.F., Barashenkov, I.V. Asymptotic expansion of the wobbling kink. Theor Math Phys 159, 863–869 (2009). https://doi.org/10.1007/s11232-009-0074-7

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  • DOI: https://doi.org/10.1007/s11232-009-0074-7

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