Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

doi:10.1088/1674-1056/22/4/040310

中国物理B ›› 2013, Vol. 22 ›› Issue (4): 40310-040310.doi: 10.1088/1674-1056/22/4/040310

Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

何俊荣, 李画眉

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2012-08-22 修回日期:2012-09-28 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
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).

Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

He Jun-Rong (何俊荣), Li Hua-Mei (李画眉)

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Received:2012-08-22 Revised:2012-09-28 Online:2013-03-01 Published:2013-03-01
Contact: Li Hua-Mei E-mail:lihuamei@zjnu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: generalized nonautonomous cubic-quintic nonlinear Schrö, dinger equation, similarity reduction, Faraday-type waves, solitary wave solution

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.

Key words: generalized nonautonomous cubic–quintic nonlinear Schrödinger equation, similarity reduction, Faraday-type waves, solitary wave solution

中图分类号: (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

03.75.Lm

05.45.Yv (Solitons)

何俊荣, 李画眉. Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients[J]. 中国物理B, 2013, 22(4): 40310-040310.

He Jun-Rong (何俊荣), Li Hua-Mei (李画眉). Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients[J]. Chin. Phys. B, 2013, 22(4): 40310-040310.

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Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

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