Analytic soliton solutions of cubic-quintic Ginzburg-Landau equation with variable nonlinearity and spectral filtering in fiber lasers

In fiber lasers, the study of the cubic-quintic complex Ginzburg-Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y-type solitons and combined solitons) of exact soliton solutions for the variable-coefficient cubic-quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split-step Fourier method and fourth-order Runge-Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variablecoefficient cubic-quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.