Pulse propagation in inhomogeneous nonlinear media with linear and nonlinear gain and loss, described by a system of nonlinearly coupled complex Ginzburg–Landau equations (CGLEs) with variable coefficients, is considered. Exact solitary pulse (SP) solutions are obtained analytically, for special choices of variable coefficients of the nonlinear gain/loss terms, by a modified Hirota bilinear method. The solutions include space– or time–dependent wave numbers, which imply dilatation or compression of the SPs. Stability of the solutions is tested by means of direct simulations, which demonstrate that, in most cases, the SPs are stable against perturbations.
Pak, O. S., Lam, C. K., Nakkeeran, K., Malomed, B., Chow, K. W., & Senthilnathan, K. (2009). Dissipative solitons in coupled complex Ginzburg-Landau equations. Journal of the Physical Society of Japan, 78, . https://doi.org/10.1143/JPSJ.78.084001