Parabolic and hyper-Gaussian similaritons in fiber amplifiers and lasers with gain saturation

We present a new asymptotically exact analytical similariton solution of the generalized nonlinear Schrdinger equation for pulses propagating in fiber amplifiers and lasers with normal dispersion including the effect of gain saturation. Numerical simulations are in excellent agreement with this analytical solution describing self-similar linearly chirped parabolic pulses. We have also found that for small enough values of the dimensionless saturation energy parameter the fiber amplifiers and lasers can generate a new type of linearly chirped self-similar pulses, which we call Hyper-Gaussian similaritons. The analytical Hyper-Gaussian similariton solution of the generalized nonlinear Schrdinger equation is also in a good agreement with numerical simulations.