The Stability Spectrum for Elliptic Solutions to the Sine-Gordon Equation

Abstract

We present an analysis of the stability spectrum for all stationary periodic solutions to the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about the spectrum are derived. Specifically, the solution parameter space is shown to be split into regions of distinct qualitative behavior of the spectrum, in one of which the solutions are stable. Additional results on the stability of solutions with respect to perturbations of an integer multiple of the solution period are given.

arXiv comment29 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1610.08539

References in corpus (3)

• The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
• Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies
• On the stability analysis of periodic sine-Gordon traveling waves

Cited by in corpus (4)

• The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
• Localized structures on librational and rotational travelling waves in the sine-Gordon equation
• Stability of elliptic solutions to the sinh-Gordon equation
• Periodic traveling waves in the ϕ^4 model: Instability, stability and localized structures