Abstract
•An extended NLSE with time-modulated coefficients is studied.•The nonautonomous bright soliton solutions are reported.•Propagation properties of those solitons are discussed.
We investigate the existence and propagation properties of envelope solitons of an extended nonlinear Schr ödinger equation with the time-modulated dispersion, quadratic-cubic nonlinearities and linear gain or loss, which govern the nonlinear wave propagation in a nonautonomous quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction. A novel class of nonautonomous bright soliton solutions on continuous-wave background is identified for the first time. It is shown that these localized structures possess interesting features that differ from the usual bright solitons. A rich variety of evolution behaviors, which include snakelike and periodic oscillating bright soliton dynamics, is revealed. The constraints of the system parameters to form these nonlinear localized structures are also suggested.