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 , 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.
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}
}