Abstract
•Stationary optical solitons with nonlinear chromatic dispersion are studied.•Quadratic–cubic nonlinearity is considered.•Both linear temporal evolution as well as generalized temporal evolution are addressed.•Solutions are in term of Appell's hypergeometric functions.•Convergence criteria are also presented.
Stationary optical solitons with quadratic–cubic law of nonlinear refractive index and nonlinear chromatic dispersion are retrieved. The model is considered with linear temporal evolution as well as with generalized temporal evolution. The results are in terms of Appell's hypergeometric function whose convergence criteria are also presented.