| Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients |
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| 引用本文： | 荆建春,李彪.Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients[J].中国物理 B,2013,22(1):10303-010303. |
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| 作者姓名： | 荆建春 李彪 |
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| 作者单位： | Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Grant No. 11041003);the Ningbo Natural Science Foundation, China (Grant No. 2009B21003);K.C. Wong Magna Fund in Ningbo University, China |
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| 摘 要： | In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (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.
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| 关 键 词： | (3+1)-dimensional nonlinear Schrö dinger equation extended symmetry exact solution symbolic computation |
| 收稿时间： | 2012-03-30 |
Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients |
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| Jing Jian-Chun and Li Biao.Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients[J].Chinese Physics B,2013,22(1):10303-010303. |
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| Authors: | Jing Jian-Chun and Li Biao |
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| Affiliation: | Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China |
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| 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. |
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| Keywords: | (3+1)-dimensional nonlinear Schrödinger equation extended symmetry exact solution symbolic computation |
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