Geodesic
Asymptotic expansion of the~wobbling kink
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 527-535

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We use the method of multiple scales to study the wobbling kink of the $\phi^4$ 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.
Keywords: $\phi^4$ equation, wobbling kink, asymptotic expansion, second-harmonic radiation. 
@article{TMF_2009_159_3_a17,
     author = {O. F. Oxtoby and I. V. Barashenkov},
     title = {Asymptotic expansion of the~wobbling kink},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {527--535},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a17/}
}
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O. F. Oxtoby; I. V. Barashenkov. Asymptotic expansion of the~wobbling kink. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 527-535. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a17/