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In this paper, based on a variable-coefficient nonlinear Schrödinger (vcNLS) equation, amplification of the fundamental and second-order unchirped solitons in the dispersion-decreasing fiber without any external amplification device, which is different from those in the existing literatures, is studied. Via symbolic computation, soliton solutions of the vcNLS equation are obtained. For a fundamental-soliton pulse, the amplitude is amplified by the gain during the propagation, whereas the width keeps unchanged. Because of the equilibrium between the gain, nonlinearity and varying dispersion, soliton structure is not destroyed, and the amplified fundamental soliton is free from the pedestal and chirp. With the increase of the absolute value of the gain coefficient $$\alpha $$ , magnification of the fundamental-soliton amplitude is enhanced in the same propagation distance. For the second-order soliton, the width is compressed and the amplitude is amplified, because the amplification process is accompanied by the compression of the soliton. Period of the second-order soliton decreases exponentially during the propagation, and decreases with the increase of the absolute value of $$\alpha $$ in the same propagation distance. [ABSTRACT FROM AUTHOR]

Coupled nonlinear Schrödinger (CNLS) equations for the fiber couplers with asymmetric self-phase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, one- and two-soliton solutions are obtained for the constant- and variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β, SPM coefficient σ, XPM coefficient σ and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that | β| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ/ σ and increase of | β| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the one- and two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ/ σ, β( z) = a e and γ( z) = a e on the optical switching are analyzed (where a, a and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of | a| and decrease of | b|, and optical extinction ratios increase with the increase of | a| and decrease of σ/ σ and | a|. [ABSTRACT FROM AUTHOR]