Analytical nonautonomous soliton solutions for the cubic–quintic nonlinear Schrödinger equation with distributed coefficients

In this paper, we find the exact bright, dark and gray analytical nonautonomous soliton solutions of the generalized CQNLSE with spatially inhomogeneous group velocity dispersion (GVD) and amplification or attenuation by the similarity transformation method under certain parametric conditions. As an example, we investigate their propagation dynamics in the soliton control system. In addition, the interaction of two neighboring solitary waves is discussed, and the results show that the interaction of two neighboring solitary waves can be restricted by choosing the distributed coefficients appropriately. Finally, the stability of the solutions is checked by direct numerical simulation.