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Some exact solitons to the (2 + 1)-dimensional Broer–Kaup–Kupershmidt system with two different methods

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Abstract

The exact solutions of the (2 + 1) dimensional Broer–Kaup–Kupershmidt (BKK) system which has been recommended to model the nonlinear and dispersive long gravity waves traveling along with the two horizontal directions in the shallow water of uniform depth were obtained. Firstly, the given system was reduced to an ordinary differential equation (ODE) with the help of the wave transformations. Then, the reduced ODE was solved with the help of two methods which are called the modified \((G^{\prime }/G)\)-expansion method and new extended generalized Kudryashov method. We checked the results with the Maple software and plotted 3D, contour and 2D plots of some obtained solutions. As a result, we obtained exact solutions that are different from each other and have not been obtained before. Results can enhance the nonlinear dynamical behavior of a given system and demonstrate the effectiveness of the employed methodology. Results will be beneficial to a large number of engineering model specialists and useful for understanding the wave motions.

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Acknowledgements

The author, Sandeep Malik, thankfully acknowledges CSIR SRF Grant: 09/1051(0028)/2018-EMR-I.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, 151401, India

    Sandeep Malik & Sachin Kumar

  2. Department of Mathematics, Faculty of Arts and Science, Bursa Uludağ University, Bursa, Turkey

    Arzu Akbulut

  3. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

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  1. Sandeep Malik
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  2. Sachin Kumar
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  3. Arzu Akbulut
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  4. Hadi Rezazadeh
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SM and AA wrote the main manuscript text and AA prepared figures. SK and HR revised the paper. All authors read and approved the final manuscript.

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Correspondence to Arzu Akbulut.

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Malik, S., Kumar, S., Akbulut, A. et al. Some exact solitons to the (2 + 1)-dimensional Broer–Kaup–Kupershmidt system with two different methods. Opt Quant Electron 55, 1215 (2023). https://doi.org/10.1007/s11082-023-05500-6

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