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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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Author information

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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Keywords

  • ϕ 4 equation
  • wobbling kink
  • asymptotic expansion
  • second-harmonic radiation