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Solitary Waves for the GeneralizedNonautonomous Dual-power NonlinearSchrödinger Equations with Variable Coeffcients
  
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KeyWord:Semi-quasi-homogeneous  quadratic system  singular point  global phase portraits
Author NameAffiliation
Haihua Liang Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 
Lijia Han Department of Mathematics and Physics, North China Electric Power Uni- versity, Beijing 102206, China 
Yehui Huang Department of Mathematics and Physics, North China Electric Power Uni- versity, Beijing 102206, China 
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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 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.