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Wobbling kinks in ϕ 4 and sine-Gordon theory

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Nonlinear Phenomena

Part of the book series: Lecture Notes in Physics ((LNP,volume 189))

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Abstract

When the ϕ 4 model admits a kink-solution, it also admits a wobbling king, which satisfies the boundary conditions of a kink, but possesses an internal degree of freedom. In this paper we develop a formal perturbation series for the wobbling kink in ϕ 4 theory, and give the first two terms in the series explicitly. Then we prove that the formal series actually is asymptotic for a rahter long time [O (K ln(1/ε)), for a certain K]. Finally, we construct an exact 3-soliton solution of the sine-Gordon equation that also has the properties of a wobbling kink. For the sine-Gordon equation, the wobbling kink seems to be mildly unstable.

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Editor information

K. B. Wolf

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© 1983 Springer-Verlag

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(1983). Wobbling kinks in ϕ 4 and sine-Gordon theory. In: Wolf, K.B. (eds) Nonlinear Phenomena. Lecture Notes in Physics, vol 189. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12730-5_11

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  • DOI: https://doi.org/10.1007/3-540-12730-5_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12730-7

  • Online ISBN: 978-3-540-38721-3

  • eBook Packages: Springer Book Archive

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