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arXiv · 1010.2759

Stability of Travelling Wave Solutions to the Sine-Gordon Equation

C. K. R. T. Jones·R. Marangell
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Abstract

We give a geometric proof of spectral stability of travelling kink wave solutions to the sine-Gordon equation. For a travelling kink wave solution of speed $c \neq \pm 1$, the wave is spectrally stable. The proof uses the Maslov index as a means for determining the lack of real eigenvalues. Ricatti equations and further geometric considerations are also used in establishing stability.

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C. K. R. T. Jones, R. Marangell. 2010-10-13. Stability of Travelling Wave Solutions to the Sine-Gordon Equation. https://arxiv.org/abs/1010.2759

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