English

Stability of Travelling Wave Solutions to the Sine-Gordon Equation

Spectral Theory 2010-10-15 v1 Analysis of PDEs

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±1c \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.

Keywords

Cite

@article{arxiv.1010.2759,
  title  = {Stability of Travelling Wave Solutions to the Sine-Gordon Equation},
  author = {C. K. R. T. Jones and R. Marangell},
  journal= {arXiv preprint arXiv:1010.2759},
  year   = {2010}
}