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The Davey–Stewartson I equation: doubly localized two-dimensional rogue lumps on the background of homoclinic orbits or constant

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General doubly localized two-dimensional lumps on a background of homoclinic orbits or constant in the Davey–Stewartson I equation are studied. These special lumps first emerge from the background and then rapidly merge into the background again after existing for a very short period. Since these lumps are localized in time as well as in two-dimensional space, and possess the features of rogue wave phenomenon in two-dimensional physics; thus, they are termed “rogue lumps”. Technically, our derivation of the rogue lumps is achieved by a generalization of tau functions into multi-component forms in the Kadomtsev–Petviashvili (KP) hierarchy reduction method, and this generalized procedure allows us to construct the solutions containing rational solitary waves, periodic solitons, dark solitons and their mixed solitons in the DSI equation. Our results are extensions of doubly localized waves in two-dimensional integrable systems and are valuable in understanding rogue wave phenomena.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant Nos. 12071304 and 11871446), the Guangdong Basic and Applied Basic Research Foundation (Grant 2022A1515012554), and the Research and Development Funds of Hubei University of Science and Technology (Grant BK202302).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, 437100, Hubei, People’s Republic of China

    Jiguang Rao

  2. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Jingsong He

  3. School of Mathematical Sciences, USTC, Hefei, 230026, Anhui, People’s Republic of China

    Yi Cheng

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  1. Jiguang Rao
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Rao, J., He, J. & Cheng, Y. The Davey–Stewartson I equation: doubly localized two-dimensional rogue lumps on the background of homoclinic orbits or constant. Lett Math Phys 112, 75 (2022). https://doi.org/10.1007/s11005-022-01571-w

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