Stability of solitary solutions to the cubic-quintic coupled nonlinear Schrödinger equation(CQCNLSE)

In this article we report the results of an investigation on the stability of solitary solutions to the Cubic-Quintic Coupled Nonlinear Schr ö dinger Equations.Using the theory of linear operators (here,2×2 matrics), we show that under a perturbation ui→ui + δui(δui= (αi(T) + ibi(T))eµδ)(i=1,2) the solitary solutions are stable. Moreover,we include the perturbation into the corresponding Hamiltonian and calculate the first and second order variations. Stability of the solitary solutions to the Coupled equations is then verified by the fact that the first- order variation vanishes and the second- order one is positive