| Abstract: |
| We consider the initial value problem to a nonlinear Schr\{o}dinger equation containing both linear amplification and cubic nonlinear dissipation. This model describes the evolution of pulses propagating through a special optical fiber providing the effect of erbium doped fiber amplifier (for short, EDFA). It is known that the nonlinear Schr\{o}dinger equation possesses a $t$-periodic uniform solution ($t$-PUS). In this talk, we discuss the stability of $t$-PUS under small perturbations in $H^1(\mathbb{T})$, where $\mathbb{T}=\mathbb{R}/ 2 \pi \mathbb{Z}$. If time permits, the bifurcation of amplitude of the $t$-PUS will be discussed. By the bifurcation analysis, a $t$-periodic solution with curved amplitude is obtained, and it \r\nis possibly applied to the information transmission through an optical fiber |
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