Stability of elliptic solutions to the sinh-Gordon equation
arXiv:2008.01876 · doi:10.1007/s00332-021-09722-4
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.