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=${\mathit{tsum}}_{\mathit{n}}$F‖${\mathrm{\Psi }}_{\mathit{n}}$${\mathrm{\Vert }}^2$dt with respect to the soliton parameter ${\lambda }^2$ is negative.

• Received 14 June 1995

DOI:https://doi.org/10.1103/PhysRevE.52.5549