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Darboux transformation and nonautonomous solitons for a generalized inhomogeneous Hirota equation

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Abstract

In this paper, a generalized inhomogeneous Hirota equation with spatial inhomogeneity and nonlocal nonlinearity is investigated in detail. Firstly, the Darboux transformation is constructed based on corresponding nonisospectral linear eigenvalue problem. This transformation has an essential difference from the isospectral case. Furthermore, the nonautonomous soliton solutions are obtained via the Darboux transformation. Finally, properties of these solutions in the inhomogeneous media are discussed graphically to illustrate the influences of the variable coefficients. It is found that the velocity and amplitude of the solitons can be controlled by the inhomogeneous parameters. Especially, a special two-soliton solution which are localized both in space and time exhibits the feature of the so-called rogue waves but with a zero background.

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Acknowledgments

This work is supported by the NSF of China with Grant Nos. 71271083, 11301179, the SSF of Beijing with Grant No. 15ZDA19, the Co-construction Project and Young Talents Plan of Beijing Municipal Commission of Education. The authors also acknowledge the support by the Fundamental Research Funds of the Central Universities with the Grant Nos. 2014ZZD08, 2014ZZD10, 2015MS56, 2016MS63. The authors would like to thank Prof. Zhang Dajun for his sincere guidance. X L Yong is also partially supported by the State Scholarship Fund of China.

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Authors and Affiliations

  1. School of Mathematical Sciences and Physics, North China Electric Power University, Beijing, 102206, China

    Y J Tian, X L Yong & Y H Huang

  2. School of Economics and Managements, North China Electric Power University, Beijing, 102206, China

    J W Gao

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  1. Y J Tian
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  2. X L Yong
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Correspondence to J W Gao.

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Tian, Y.J., Yong, X.L., Huang, Y.H. et al. Darboux transformation and nonautonomous solitons for a generalized inhomogeneous Hirota equation. Indian J Phys 91, 129–138 (2017). https://doi.org/10.1007/s12648-016-0903-0

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