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Chin. Phys. B, 2013, Vol. 22(4): 040310    DOI: 10.1088/1674-1056/22/4/040310
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Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

He Jun-Rong, Li Hua-Mei
Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract  A class of analytical solitary-wave solutions to the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients and potentials are constructed by using the similarity transformation technique. Constraints for the dispersion coefficient, the cubic and quintic nonlinearities, the external potential, and the gain (loss) coefficient are presented at the same time. Various shapes of analytical solitary-wave solutions which have important applications of physical interest are studied in detail, such as the solutions in Feshbach resonance management with harmonic potentials, Faraday-type waves in the optical lattice potentials, localized solutions supported by the Gaussian-shaped nonlinearity. The stability analysis of the solutions is discussed numerically.
Keywords:  generalized nonautonomous cubic–quintic nonlinear Schrödinger equation      similarity reduction      Faraday-type waves      solitary wave solution     
Received:  22 August 2012      Published:  01 March 2013
PACS:  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
  05.45.Yv (Solitons)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175158) and the Natural Science Foundation of Zhejiang Province of China (Grant No. LY12A04001).
Corresponding Authors:  Li Hua-Mei     E-mail:  lihuamei@zjnu.cn

Cite this article: 

He Jun-Rong, Li Hua-Mei Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients 2013 Chin. Phys. B 22 040310

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