Schrِdinger ordinary solitons and chirped solitons: fourth-order dispersive effects and cubic-quintic nonlinearity

In the framework of the one-dimensional (1D) generalized nonlinear Schrödinger equation (GNSE) including fourth-order dispersive effects and the cubic-quintic local nonlinearity, a novel class of bright solitons whose phase changes nonlinearly with spatial (or temporal) coordinate (chirped solitons) is investigated. The exact chirped soliton solutions are presented for some fixed ratio of the GNSE coefficients. Analytical methods including the variational approach are applied to predict the existence conditions and the stability properties of the chirped and ordinary solitons. Conditions for an absence of Cherenkov radiation by moving soliton have been found. Spatial–temporal wave packet dynamics in the vicinity of the stationary (soliton) solution was studied both analytically and numerically.