Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients

doi:10.1088/1674-1056/22/1/010303

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 10303-010303.doi: 10.1088/1674-1056/22/1/010303

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients

荆建春, 李彪

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2012-03-30 修回日期:2012-06-25 出版日期:2012-12-01 发布日期:2012-12-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11041003), the Ningbo Natural Science Foundation, China (Grant No. 2009B21003), and K.C. Wong Magna Fund in Ningbo University, China.

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients

Jing Jian-Chun (荆建春), Li Biao (李彪)

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2012-03-30 Revised:2012-06-25 Online:2012-12-01 Published:2012-12-01
Contact: Li Biao E-mail:biaolee2000@yahoo.com.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11041003), the Ningbo Natural Science Foundation, China (Grant No. 2009B21003), and K.C. Wong Magna Fund in Ningbo University, China.

摘要/Abstract

摘要： In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrödinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.

关键词: (3+1)-dimensional nonlinear Schrö, dinger equation, extended symmetry, exact solution, symbolic computation

Abstract: In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrödinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.

Key words: (3+1)-dimensional nonlinear Schrödinger equation, extended symmetry, exact solution, symbolic computation

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

11.30.-j (Symmetry and conservation laws) 02.70.Wz (Symbolic computation (computer algebra))

荆建春, 李彪. Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients[J]. Chin. Phys. B, 2013, 22(1): 10303-010303.

Jing Jian-Chun (荆建春), Li Biao (李彪). Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients[J]. Chin. Phys. B, 2013, 22(1): 10303-010303.

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Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients

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