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Bilinear form and Pfaffian solutions for a (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics and plasma physics

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Abstract

In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is investigated. Bilinear form under certain coefficient constraints is given via the Hirota method. The Nth-order Pfaffian solutions are proved by means of the Pfaffian technique, where N is a positive integer. N-soliton and the higher-order breather solutions are exported through the Nth-order Pfaffian solutions. Different two-soliton/breather structures and their dynamics are derived. Elastic/inelastic interactions between the two solitons/breathers are investigated. Graphical representations of the influence of the coefficients in the equation on the velocities and amplitudes of the solitons and breathers are exhibited.

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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 Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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

    Chong-Dong Cheng, Bo Tian, Yuan Shen & Tian-Yu Zhou

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  1. Chong-Dong Cheng
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Cheng, CD., Tian, B., Shen, Y. et al. Bilinear form and Pfaffian solutions for a (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics and plasma physics. Nonlinear Dyn 111, 6659–6675 (2023). https://doi.org/10.1007/s11071-022-08189-6

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