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Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

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Abstract

In this work, we study a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation for the nonlinear dispersive waves in an inhomogeneous medium. Bilinear form and N-soliton solutions are derived, where N is a positive integer. The higher-order breather and lump solutions are constructed based on the N-soliton solutions. Hybrid solutions comprising the solitons and breathers, breathers and lumps, as well as solitons and lumps are worked out. Amplitudes and velocities of the one solitons as well as periods of the first-order breathers are investigated. Amplitudes of the first-order lumps reach the maximum and minimum values at certain points given in the paper. Interactions between any two of those waves are discussed graphically.

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Notes

  1. To obtain a second-order breather whose component breathers are perpendicular or parallel with each other, the parameters in Solutions (8) should satisfy Condition (17) or (18), respectively.

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Acknowledgements

We express our sincere thanks to the Editors, Referees and all the members of our discussion group for their valuable comments.

Funding

This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, and by the Fundamental Research Funds for the Central Universities.

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Correspondence to Yi-Tian Gao or Xin Yu.

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Wang, D., Gao, YT., Yu, X. et al. Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Nonlinear Dyn 104, 1519–1531 (2021). https://doi.org/10.1007/s11071-021-06329-y

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