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Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation

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Abstract

Variable coefficients (3+1)-generalized shallow water wave equation (GSWE) is investigated via modified Hirota bilinear method. This method is presented for the first time. Compared with other methods, it solves solution without setting solution and calculates transformations without making logarithmic transformations. The rational transformation is first utilized to transform GSWE. According to homogeneous balance principle, the relation between F and G in rational transformation can be calculated by utilizing. Solutions that included rogue wave solutions, interaction solutions, breather solutions and so on, are obtained and depicted graphically. Figures are given out to the dynamic characteristics of the solution. Furthermore, the results obtained demonstrate that this approach is more direct, generalized, effective and holds for many nonlinear partial differential equations.

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Data availability

The datasets generated analyzed during the current study are not publicly available, but are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant numbers 11561051).

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Authors and Affiliations

  1. College of Sciences, Inner Mongolia University of Technology, Hohhot, People’s Republic of China

    Tianle Yin, Zhanqing Xing & Jing Pang

  2. Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Hohhot, People’s Republic of China

    Jing Pang

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  1. Tianle Yin
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  2. Zhanqing Xing
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  3. Jing Pang
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Tianle Yin and Jing Pang. The first draft of the manuscript was written by Tianle Yin and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Jing Pang.

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Yin, T., Xing, Z. & Pang, J. Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation. Nonlinear Dyn 111, 9741–9752 (2023). https://doi.org/10.1007/s11071-023-08356-3

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