In this article, the emphasis will be on the analytical investigation of the criterion of stability of solitary solutions of the cubic–quintic coupled non-linear Schrödinger equations (CQCNLSE) governing on the dispersion of electromagnetic pulses in non-linear dielectric medias (non-linear optical fiber) in which there are more than one-mode (because of the presence of binary breakdown of medias or two orthogonal polarized waves). These equations in a special occasion, in which the field amplitudes in two perpendicular directions are equal, possess the solitary solutions. By applying operator theory we will show that the solitary solutions remain stable under subsequent perturbations. Also, we will show that under subsequent perturbations, the first-order Hamiltonian variation of the two coupled fields remains zero and its second-order variation will be positive. Finally, regarding these two notions, it will be concluded that in spite of the coupling of the fields, the solitary solutions of these equations remain stable under subsequent perturbations.

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