Abstract
This paper presents evolution of super-Gaussian optical pulses to bell-shaped dissipative solitons in a lossy, cubic-quintic nonlinear (parabolic law) fiber in presence of bandwidth limited amplification. Lagrangian and Rayleigh dissipative function based variational principle leads to a set of evolution equations of individual pulse parameters that determine the condition of stable dissipative soliton pulse propagation. After some initial fluctuations, a flat-top pulse transforms its profile to a bell-shaped one and start propagating in a stable manner. In support of this analytical result, numerical investigations are performed using split-step Fourier method. In this case too, super-Gaussian pulses undergo an initial transition stage before achieving stable bell-shaped solitonic state. Dissipative solitons, thus generated, are found to be robust. This work provides the theoretical backup to experimental procedures of obtaining fundamental soliton from arbitrary pulse using a nonlinear optical fiber.