Stability of one-dimensional array solitons

The array soliton stability in the discrete nonlinear Schrodinger equation with dispersion for periodic boundary conditions is studied. The linear growth rate dependence on the discrete wave number and soliton amplitude is calculated from the linearized eigenvalue problem using the variational method. In addition, the eigenvalue problem is solved numerically by shooting method and a good agreement with the analytical results is found. It is proved numerically that the results fur the instability threshold fur the circular array coincides with the quasicollapse threshold for the case of open arrays With initial pulses in a form of array solitons.