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Mechanisms of nonlinear wave transitions in the (2+1)-dimensional generalized breaking soliton equation

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Abstract

We study the transformed nonlinear waves of the (2+1)-dimensional generalized breaking soliton (gBS) equation by analyzing characteristic lines. The N-soliton solution of the gBS equation is obtained by virtue of the Hirota bilinear method, from which the 1-order and 2-order breather wave solutions of the gBS equation are derived by the complexification method. Then, we obtain the condition of the breather wave transformation analytically. Under the condition that the two characteristic lines of the 1-order breather wave are parallel to each other, we show that the 1-order breather wave can be converted into many other types of nonlinear waves, such as M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, quasi-periodic soliton, etc. Moreover, we give four deformation modes of the 2-order breather wave, including intersection mode of a transformed wave and a breather wave; parallel mode of a transformed wave and a breather wave; intersection mode of two transformed waves; parallel mode of two transformed waves. Finally, we present the graphical analysis of the resulting solutions in order to better understand their dynamical behaviors.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 11975306, the Natural Science Foundation of Jiangsu Province under Grant No. BK20181351, the Six Talent Peaks Project in Jiangsu Province under Grant No. JY-059, and the Fundamental Research Fund for the Central Universities under the Grant Nos. 2019ZDPY07 and 2019QNA35.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Fu-Fu Ge & Shou-Fu Tian

  2. Foundation Department, Xuzhou Vocational College of Industrial Technology, Xuzhou, 221140, People’s Republic of China

    Fu-Fu Ge

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Correspondence to Shou-Fu Tian.

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Ge, FF., Tian, SF. Mechanisms of nonlinear wave transitions in the (2+1)-dimensional generalized breaking soliton equation. Nonlinear Dyn 105, 1753–1764 (2021). https://doi.org/10.1007/s11071-021-06672-0

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