Exact solutions in nonlinearly coupled cubic–quintic complex Ginzburg–Landau equations

Exact analytical solutions for pulse propagation in a nonlinear coupled cubic–quintic complex Ginzburg–Landau equations are obtained. Three families of solitary waves which describe the evolutions of progressive bright–bright, front–front, dark–dark and other families of solitary waves are investigated. These exact solutions are analyzed both for competition of loss or gain due to nonlinearity and linearity of the system. The stability of the solitary waves is examined using analytical and numerical methods. The results reveal that the solitary waves obtained here can propagate in a stable way under slight perturbation of white noise and the disturbance of parameters of the system.

► We study exact solutions for pulse propagation in a nonlinear coupled cubic–quintic complex Ginzburg–Landau equations.
► We use the Hirotaʼs method to get these exact solutions.
► The bright–bright, dark–dark, front–front waves are found and their stability analysis has been carried out.