The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg-de Vries equation

The stability of the elliptic solutions to the defocusing complex modified Korteweg- de Vries (cmKdV) equation is studied. 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 seven conserved quantities produces a Lyapunov functional, which implies that the elliptic solutions are orbitally stable with respect to the subharmonic perturbations.(c) 2022 Elsevier Ltd. All rights reserved.