Stability of Travelling Wave Solutions to the Sine-Gordon Equation
C.K.R.T. Jones, and R. Marangell
TL;DR
This paper proves the spectral stability of travelling kink wave solutions to the sine-Gordon equation using geometric methods, including the Maslov index, Ricatti equations, and other geometric considerations.
Contribution
It provides a geometric proof of spectral stability for travelling kink waves in the sine-Gordon equation, extending understanding of their stability properties.
Findings
Travelling kink waves with speed c ≠ ±1 are spectrally stable.
The proof employs the Maslov index to rule out real eigenvalues.
Geometric methods are effective in analyzing wave stability.
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.
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Taxonomy
TopicsNonlinear Photonic Systems · Nonlinear Waves and Solitons · Advanced Mathematical Physics Problems