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.