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Bäcklund transformation and conservation laws for the variable-coefficient N-coupled nonlinear Schrödinger equations with symbolic computation

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Abstract

Considering the integrable properties for the coupled equations, the variable-coefficient Ncoupled nonlinear Schrödinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bäcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, P. R. China

    Xiang Hua Meng, Bo Tian, Tao Xu & Hai Qiang Zhang

  2. Department of Mathematics, School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, P. R. China

    Xiang Hua Meng

Authors
  1. Xiang Hua Meng
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  2. Bo Tian
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  3. Tao Xu
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  4. Hai Qiang Zhang
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Correspondence to Xiang Hua Meng.

Additional information

Supported by the Foundation of Beijing Information Science and Technology University (Grant No. 1025020), Scientific Research Project of Beijing Educational Committee (Grant No. SQKM201211232016), Natural Science Foundation of Beijing (Grant No. 1102018), National Natural Science Foundation of China (Grant No. 61072145), Key Project of Chinese Ministry of Education (Grant No. 106033), and National Basic Research Program of China (973 Program) (Grant No. 2005CB321901)

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Meng, X.H., Tian, B., Xu, T. et al. Bäcklund transformation and conservation laws for the variable-coefficient N-coupled nonlinear Schrödinger equations with symbolic computation. Acta. Math. Sin.-English Ser. 28, 969–974 (2012). https://doi.org/10.1007/s10114-011-0531-8

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  • DOI: https://doi.org/10.1007/s10114-011-0531-8

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