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New interaction of high-order breather solutions, lump solutions and mixed solutions for (3+1)-dimensional Hirota–Satsuma–Ito-like equation

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Abstract

Under investigation in this letter is an (3+1)-dimensional Hirota–Satsuma–Ito-like equation, which provide strong support for studying the dynamic behavior of nonlinear waves. Based on a special Cole–Hopf transformation and Hirota bilinear method, the bilinear form of the equation is obtained and this form has never been given. High-order breather solutions, lump solutions and mixed solutions are obtained by using complex conjugate parameters and long-wave limit method. Then, the influence of the coefficient \(g_{t}(t)\) of the bilinear equation on the interaction of these solutions is analyzed by means of images. It can be found that \(g_{t}(t)\) changes the interaction of the solutions by influencing the positions and trajectories of higher-order breather solutions, lump solutions and mixed solutions. We find that different values of g(t) make the interaction of solutions different. Finally, the mixed solution of the equation including a breather wave and a line rogue wave is obtained by using the test function, and its dynamic properties are illustrated by means of images.

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Acknowledgements

We express our sincere thanks to the editors, reviewers and members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11361040, Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No. 2020LH01008 and Research and Innovation Fund for Postgraduates of Inner Mongolia Normal University under Grant No. CXJJS20089.

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  1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot, 010022, People’s Republic of China

    Shijie Zhang & Taogetusang Bao

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  1. Shijie Zhang
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Correspondence to Taogetusang Bao.

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Zhang, S., Bao, T. New interaction of high-order breather solutions, lump solutions and mixed solutions for (3+1)-dimensional Hirota–Satsuma–Ito-like equation. Nonlinear Dyn 106, 2465–2478 (2021). https://doi.org/10.1007/s11071-021-06895-1

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