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Degenerate solutions for the spatial discrete Hirota equation

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Abstract

In this paper, some degenerate solutions of the spatial discrete Hirota equation are constructed via the degenerate idea of positon solution. Under the zero seed solution, the n-positon is obtained by N-fold degenerate Darboux transformation (DT). The degenerate DT is taking the degenerate limit \(\lambda _{j}\rightarrow \lambda _{1}\) for the eigenvalues \(\lambda _{j}(j=1,2, 3, \ldots , N)\) of N-fold DT and then performing the high-order Taylor expansion near \(\lambda _{1}\). Considering the universal Darboux transformation, breather is obtained from the nonzero seed. Then, a new type of breather solution can be produced by using the same degenerated method and higher-order Taylor expansion for eigenvalues in determinant expression of breather solution. The explicit determinants of breather-positon solution and positon solution are constructed, respectively, and the complicated and significant dynamics of low-order solution are also revealed.

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Acknowledgements

The authors would like to thank Dr. Guo Lijuan of Nanjing Forestry University for the fruitful suggestions. This work is supported by the NSF of Zhejiang Province under Grant No. LY15A010005, the NSF of Ningbo under Grant No. 2018A610197, the NSF of China under Grant No. 11671219 and K. C. Wong Magna Fund in Ningbo University.

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  1. School of Mathematics and Statistics, Ningbo University, Zhejiang, 315211, People’s Republic of China

    Meng Li & Maohua Li

  2. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Jingsong He

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  1. Meng Li
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Li, M., Li, M. & He, J. Degenerate solutions for the spatial discrete Hirota equation. Nonlinear Dyn 102, 1825–1836 (2020). https://doi.org/10.1007/s11071-020-05973-0

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