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Interactions among the Rogue Waves and Solitons for a (2+1)-dimensional Maccari System in Fluid Mechanics and Nonlinear Optics

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Abstract

In this paper, we investigate a (2+1)-dimensional Maccari system in fluid mechanics and nonlinear optics. With the aid of the bilinear method and Kadomtsev-Petviashvili hierarchy reduction, we construct the semi-rational solutions. Based on the semi-rational solutions, hybrid solutions which illustrate the interactions among the Nth-order rogue waves and \((N + 1)\) solitons are obtained, where N is a positive integer. Due to the interactions, the rogue waves in those hybrid solutions behave localized in two-dimensional space and in time. Hybrid solutions consisting of the first-order rogue wave and two solitons, and hybrid solutions consisting of the second-order rogue waves and three solitons are shown. There are two types of the rogue waves: the line rogue waves and rogue waves. For the hybrid solutions consisting of the first-order rogue wave and two solitons, the asymptotic forms and amplitudes of the two solitons are given. Furthermore, we study the relations between the amplitudes of the two types of rogue waves and the soliton phase parameters graphically. For the hybrid solutions consisting of the second-order rogue waves and three solitons, three different types of the line rogue waves or rogue waves are derived upon the relations among the soliton phase parameters.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yu Zhao, Bo Tian, Cong-Cong Hu, Su-Su Chen & Shao-Hua Liu

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  1. Yu Zhao
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Zhao, Y., Tian, B., Hu, CC. et al. Interactions among the Rogue Waves and Solitons for a (2+1)-dimensional Maccari System in Fluid Mechanics and Nonlinear Optics. Qual. Theory Dyn. Syst. 22, 136 (2023). https://doi.org/10.1007/s12346-023-00824-w

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