Stability of elliptic solutions to the sinh-Gordon equation

Abstract

Using the integrability of the sinh-Gordon equation, we demonstrate the spectral stability of its elliptic solutions. By constructing a Lyapunov functional using higher-order conserved quantities of the sinh-Gordon equation, we show that these elliptic solutions are orbitally stable with respect to subharmonic perturbations of arbitrary period.

References in corpus (4)

• The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
• Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes
• On the stability analysis of periodic sine-Gordon traveling waves
• The Stability Spectrum for Elliptic Solutions to the Sine-Gordon Equation

Cited by in corpus (1)

• Periodic traveling waves in the ϕ^4 model: Instability, stability and localized structures