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Determinant representation of Darboux transformation for the AKNS system

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Abstract

The n-fold Darboux transform (DT) is a 2×2 matrix for the Ablowitz-Kaup-Newell-Segur (AKNS) system. In this paper, each element of this matrix is expressed by 2n + 1 ranks’ determinants. Using these formulae, the determinant expressions of eigenfunctions generated by the n-fold DT are obtained. Furthermore, we give out the explicit forms of the n-soliton surface of the Nonlinear Schrodinger Equation (NLS) by the determinant of eigenfunctions.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    He Jingsong, Zhang Ling, Cheng Yi & Li Yishen

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  1. He Jingsong
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  2. Zhang Ling
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  3. Cheng Yi
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  4. Li Yishen
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Correspondence to He Jingsong.

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He, J., Zhang, L., Cheng, Y. et al. Determinant representation of Darboux transformation for the AKNS system. SCI CHINA SER A 49, 1867–1878 (2006). https://doi.org/10.1007/s11425-006-2025-1

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  • DOI: https://doi.org/10.1007/s11425-006-2025-1

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