Solitary Waves for the Generalized Nonautonomous Dual-power Nonlinear Schrödinger Equations with Variable Coeffcients

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 ma- terials such as LiNbO3, as well as many nonlinear optics problems. We gen- eralize an explicit similarity transformation, which maps generalized nonau- tonomous DPNLS equations into ordinary autonomous DPNLS. Moreover, solitary waves of two concrete equations with space-quadratic potential and optical super-lattice potential are investigated.     

Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems

This paper study the planar quadratic semi-quasi-homogeneous polynomial systems(short for PQSQHPS). By using the nilpotent singular points theorem, blow-up technique, Poincaré index formula, and Poincaré compaction method, the global phase portraits of such systems in canonical forms are discussed. Furthermore, we show that all the global phase portraits of PQSQHPS can be-classed into six topological equivalence classes.