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Solitons, breathers and rational solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation

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Abstract

This paper explores the Konopelchenko–Dubrovsky (KD) equation and employs Hirota’s bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique to construct solitons, line breathers, rational solutions, and algebraic solitons within the system. These solutions are represented using \(N \times N\) determinants. When the determinant size N is odd, periodic background solutions are generated, while even N values yield solutions on constant backgrounds. By utilizing asymptotic analysis, the paper elucidates explicit expressions for asymptotic algebraic solitons localized in a straight line for the algebraic soliton solutions. The dynamics of the obtained solutions are further examined and illustrated through plots.

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Acknowledgements

The authors are very grateful to all the members of our discussion group. This work has been supported by the National Natural Science Foundation of China (Nos. 12001241, 72174091); the Basic Research Program of Jiangsu Province (No. BK20230307); the Basic science research project of higher education in Jiangsu Province (No. 22KJB110014); the National Key R &D Program of China (No. 2020YFA0608601); the Major programs of the National Social Science Foundation of China (No. 22 &ZD136).

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Authors and Affiliations

  1. School of physical and mathematical sciences, Nanjing Tech University, Nanjing, 211816, Jiangsu, China

    Min-Jie Dong & Wei Shi

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, Jiangsu, China

    Li-Xin Tian

  3. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Li-Xin Tian & Jing-Dong Wei

  4. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, 210023, Jiangsu, China

    Yun Wang

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  1. Min-Jie Dong
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Dong, MJ., Tian, LX., Shi, W. et al. Solitons, breathers and rational solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09583-y

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