  The stability of the elliptic solutions to the defocusing complex modified
Korteweg-de Vries (cmKdV) equation is studied. The orbital stability of the
cmKdV equation was established in [19] when the periodic orbits do not
oscillate around zero. In this paper, we study the periodic solutions
corresponding to the case that the orbits oscillate around zero. Using the
integrability of the defocusing cmKdV equation, we prove the spectral stability
of the elliptic solutions. We show that one special linear combination of the
first five conserved quantities produces a Lyapunov functional, which implies
that the elliptic solutions are orbitally stable with respect to the
subharmonic perturbations.
