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N-soliton, Hth-order breather, hybrid and multi-pole solutions for a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid

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Abstract

In this paper, we investigate a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid. Via the Hirota method, we obtain certain bilinear forms and N-soliton solutions, where N is a positive integer. We also derive the Hth-order breather and hybrid solutions through the complex conjugated transformations, where H is a positive integer. Moreover, multi-pole solutions are constructed with the limit method. Multi-soliton, breather-breather, soliton-breather and multi-pole interactions are studied. Influences of the external force and variable coefficients on the solutions are discussed analytically and graphically. For those nonlinear waves: (i) the external force affects the backgrounds and velocities; (ii) the damping coefficient affects the amplitudes, widths and velocities; (iii) the dispersive and dissipative coefficients affect the characteristic lines and velocities.

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Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11772017.

Funding

This work has been supported by the National Natural Science Foundation of China under Grant. 11772017.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Hao-Dong Liu, Bo Tian, Yu-Qi Chen, Chong-Dong Cheng & Xiao-Tian Gao

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Correspondence to Bo Tian.

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Liu, HD., Tian, B., Chen, YQ. et al. N-soliton, Hth-order breather, hybrid and multi-pole solutions for a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid. Nonlinear Dyn 113, 3655–3672 (2025). https://doi.org/10.1007/s11071-024-10397-1

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