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Nonautonomous lump waves of a (3+1)-dimensional Kudryashov–Sinelshchikov equation with variable coefficients in bubbly liquids

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Abstract

In this paper, we study the (3+1)-dimensional variable-coefficient Kudryashov–Sinelshchikov (vc-KS) equation, which characterizes the evolution of nonautonomous nonlinear waves in bubbly liquids. The nonautonomous lump solutions of the vc-KS equation are produced via the Hirota bilinear technique. The characteristics of trajectory and velocity of this wave are analyzed with variable dispersion coefficients. Based on the positive quadratic function assumption, we further discuss two types of interactions between the soliton and lump under the periodic and exponential modulations. Then, we give the breathing lump waves showing the periodic oscillation behavior. Finally, we obtain the second-order nonautonomous lump solution, which also shows periodic interactions if we select trigonometric functions as the dispersion coefficients.

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Acknowledgements

Zhengran Hu and Feifan Wang are co-first authors. We express our sincere thanks to all members of our discussion group for their valuable comments. The authors would like to thank Prof. L. W. for his suggestions on the topic, structure and analysis. This work has been supported by the Natural Science Foundation of Beijing Municipality under Grant No. 1212007, the Fundamental Research Funds for the Central Universities under No. 2020MS043, the Special Funds for the Local Science and Technology Development of the Central Government under Grant No. 2020ZY0014 and the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No. NJYT-19-B21.

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  1. School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Zhengran Hu, Feifan Wang, Yinchuan Zhao & Min Li

  2. School of Computation Information Management, Inner Mongolia University of Finance and Economics, Hohhot, 010070, People’s Republic of China

    Zhongzhou Lan

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  1. Zhengran Hu
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Hu, Z., Wang, F., Zhao, Y. et al. Nonautonomous lump waves of a (3+1)-dimensional Kudryashov–Sinelshchikov equation with variable coefficients in bubbly liquids. Nonlinear Dyn 104, 4367–4378 (2021). https://doi.org/10.1007/s11071-021-06570-5

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