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Studies on the breather solutions for the \(\mathbf{(2+1)}\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluids and plasmas

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Abstract

In this paper, we study the \((2 + 1)\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which has certain applications in fluids and plasmas. Via the Kadomtsev–Petviashvili hierarchy reduction, we derive two types of the breather solutions in terms of Gramian. Based on the first type breather solutions, we observe the breathers and periodic waves, while we observe the breathers and solitons according to the second type breather solutions. Taking the long-wave limits technique for the first type breather solutions, we derive semi-rational and rational solutions. The semi-rational solutions describe the interactions between the rogue waves/lumps and breathers, while the rational solutions give birth to the rogue waves and lumps.

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Notes

  1. Determinant solutions for the NLEEs can be expressed by Gramian, and the Gramian is as the determinant of a Gram matrix whose matrix entries are in the integral expression [26, 27, 42]. It has been proved that the bilinear KP equation could be reduced to a Jacobi identity by taking its solution as a Gramian [42].

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. Xiao-Yu Wu has been supported by “the Fundamental Research Funds for the Central Universities” No. BLX201927, Funded by China Postdoctoral Science Foundation under Grant No. 2019M660491.

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  1. School of Science, Dalian Maritime University, Dalian, 116026, People’s Republic of China

    Yan Sun

  2. School of Science, Beijing Forestry University, Beijing, 100873, People’s Republic of China

    Xiao-Yu Wu

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Sun, Y., Wu, XY. Studies on the breather solutions for the \(\mathbf{(2+1)}\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluids and plasmas. Nonlinear Dyn 106, 2485–2495 (2021). https://doi.org/10.1007/s11071-021-06917-y

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