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The semi-rational solutions of the (2+1)-dimensional cmKdV equations

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Abstract

The (\(2+1\))-D complex modified Korteweg–de Vries (cmKdV) equations are investigated with the aid of the Darboux transformation method. Through the limits \(\lambda _{2k-1}\rightarrow \lambda _0=-\frac{a}{2}+ci\,(k=1,\ldots ,m,\,m\leqslant n-1)\), the order-n semi-rational solutions are obtained. The order-2 semi-rational solutions and order-3 semi-rational solutions are analyzed in detail. By changing different parameters \(l_j\), different semi-rational solutions are deduced, including rogue wave interaction with the periodic wave or breather and lump interaction with the periodic wave or breather. The dynamical properties of these solutions are discussed, which indicates that these interactions are elastic collisions. In terms of application, these semi-rational solutions will be valuable in modeling physical problems.

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Acknowledgements

This work is sponsored by NUPTSF (Grant No. NY220161), the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No. JSSCBS20210541), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No. 22KJB110004), and the National Natural Science Foundation of China (Grant No. 11871446).

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  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Feng Yuan

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Yuan, F. The semi-rational solutions of the (2+1)-dimensional cmKdV equations. Nonlinear Dyn 111, 733–744 (2023). https://doi.org/10.1007/s11071-022-07849-x

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