Abstract
We investigate the propagation of self-similar optical solitons on a continuous-wave background through a non-centrosymmetric waveguide with second- and third-order nonlinearities. The generalized inhomogeneous nonlinear Schrödinger equation with quadratic–cubic nonlinearities and gain or loss is used to describe the beam propagation through the waveguide. Three new types of exact self-similar localized solutions propagating on a continuous-wave background are found under certain parametric conditions. The self-similar wave solutions comprise bright solitons, W-shaped, and kink solitons. The dynamic behaviors of these solitons are analyzed for a periodically distributed dispersion system.
•Self-similar optical solitons with continuous-wave background are studied.•The self-similar wave solutions comprise bright solitons, W-shaped, and kink solitons.•The dynamic behaviors of these solitons are analyzed.