Stability of solitary waves for the generalized nonautonomous dual-power nonlinear Schrödinger equations with time-dependent coefficients

•Generalized nonautonomous dual-power nonlinear Schrodinger (DPNLS) equations with time-dependent coefficients have interesting features and potential applications in nonlinear optics and BECs.•Solitary waves of the generalized nonautonomous (DPNLS) equations are explicitly obtained.•Stability of the solitary waves for the generalized nonautonomous (DPNLS) equations is strictly proved by Vakhitov-Kolokolov stability criterion.•Stability for three concrete nonautonomous dual-power nonlinear Schrodinger equations with clear physical background are investigated.

In this paper, we explicitly obtain the solitary waves of the generalized nonautonomous dual-power nonlinear Schrödinger equations (DPNLS) with time-dependent coefficients. The stability of the solitary waves of the nonautonomous DPNLS is strictly proved by Vakhitov-Kolokolov stability criterion. Finally, we show solitary waves of three interesting examples to test our stability conditions.