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Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov–Ivanov equation under the zero/nonzero background

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Abstract

In this article, the inverse scattering transform is considered for the Gerdjikov–Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann–Hilbert (RH) method. The formula of the soliton solutions is established by Laurent expansion to the RH problem. The method we used is different from computing solution with simple poles since the residue conditions here are hard to be obtained. The formula of multiple soliton solutions with one high-order pole and N multiple high-order poles are obtained, respectively. The dynamical properties and characteristic for the high-order pole solutions are further analyzed.

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Acknowledgements

This work is supported by the National Science Foundation of China (Grant Nos. 11671095, 51879045).

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Authors and Affiliations

  1. School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, People’s Republic of China

    Zechuan Zhang & Engui Fan

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  1. Zechuan Zhang
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  2. Engui Fan
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Correspondence to Engui Fan.

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Zhang, Z., Fan, E. Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov–Ivanov equation under the zero/nonzero background . Z. Angew. Math. Phys. 72, 153 (2021). https://doi.org/10.1007/s00033-021-01583-x

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  • DOI: https://doi.org/10.1007/s00033-021-01583-x

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