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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 |
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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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Received: 30 March 2012
Revised: 25 June 2012
Accepted manuscript online:
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PACS:
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03.65.Ge
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(Solutions of wave equations: bound states)
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11.30.-j
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(Symmetry and conservation laws)
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02.70.Wz
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(Symbolic computation (computer algebra))
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Fund: 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. |
Corresponding Authors:
Li Biao
E-mail: biaolee2000@yahoo.com.cn
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Cite this article:
Jing Jian-Chun (荆建春), Li Biao (李彪) Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients 2013 Chin. Phys. B 22 010303
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