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Bilinear form and soliton interactions for the modified Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

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Abstract

In this paper, we investigate the modified Kadomtsev–Petviashvili (mKP) equation for the nonlinear waves in fluid dynamics and plasma physics. By virtue of the rational transformation and auxiliary function, new bilinear form for the mKP equation is constructed, which is different from those in previous literatures. Based on the bilinear form, one- and two-soliton solutions are obtained with the Hirota method and symbolic computation. Propagation and interactions of shock and solitary waves are investigated analytically and graphically. Parametric conditions for the existence of the shock, elevation solitary, and depression solitary waves are given. From the two-soliton solutions, we find that the (i) parallel elastic interactions can exist between the (a) shock and solitary waves, and (b) two elevation/depression solitary waves; (ii) oblique elastic interactions can exist between the (a) shock and solitary waves, and (b) two solitary waves; (iii) oblique inelastic interactions can exist between the (a) two shock waves, (b) two elevation/depression solitary waves, and (c) shock and solitary waves.

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Notes

  1. Oblique solitons mean that there exists a nonzero angle between the two solitons when they interact [15].

  2. Note that bilinear form (3a), (3b), (3c) is a new one, which is different from those obtained with the double logarithmic transformation in [28, 40].

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Acknowledgements

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

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Authors and Affiliations

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

    Yan Jiang, Bo Tian, Pan Wang & Min Li

  2. School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing, 100876, China

    Yan Jiang, Bo Tian, Pan Wang & Min Li

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  1. Yan Jiang
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Correspondence to Bo Tian.

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Jiang, Y., Tian, B., Wang, P. et al. Bilinear form and soliton interactions for the modified Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Nonlinear Dyn 73, 1343–1352 (2013). https://doi.org/10.1007/s11071-013-0867-y

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