Analytic criterion for soliton instability in a nonlinear fiber array

The stability problem for the so-called continuous-discrete solitons in a nonlinear fiber array is examined. We prove that the ground states are unstable if the first derivative of the ``energy'' integral P=tsumₙF{}Ψₙ{{{}}}²$dt with respect to the soliton parameter ${{λ}}²$ is negative.