Solitary Waves for the Generalized Nonautonomous Dual-Power Nonlinear Schrödinger Equations with Variable Coefficients

Abstract

In this paper, we study the solitary waves for the generalized nonautonomous dual-power nonlinear Schrödinger equations (DPNLS) with variable coefficients, which could be used to describe the saturation of the nonlinear refractive index and the solitons in photovoltaic-photorefractive materials such as LiNbO3, as well as many nonlinear optics problems. We generalize an explicit similarity transformation, which maps generalized nonautonomous DPNLS equations into ordinary autonomous DPNLS. Moreover, solitary waves of two concrete equations with space-quadratic potential and optical super-lattice potential are investigated.