Stability of Elliptic Solutions to the sinh-Gordon Equation

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