Stability of the soliton states in a nonlinear fiber coupler

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Abstract
A detailed study of the stability of the soliton states for a nonlinear fiber coupler is presented. It is shown that the stability of the symmetric soliton states is delimited by the point of bifurcation: symmetric states are stable starting from zero energy up to the point of bifurcation, and unstable beyond the point of bifurcation. Asymmetric A-type states are stable at points with positive slope in the energy dispersion curve, and unstable otherwise. B-type asymmetric states are always unstable. Antisymmetric soliton states have regions of unstable as well as stable behavior. Moreover, the perturbation growth rate for the antisymmetric states can be complex in a certain range of spatial frequencies. A close analogy between the stability results for the soliton states in a nonlinear coupler and those for guided waves in planar nonlinear structures is established.