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Elastic Two-Kink, Breather, Multiple Periodic, Hybrid and Half-/Local-Periodic Kink Solutions of a Sharma-Tasso-Olver-Burgers Equation for the Nonlinear Dispersive Waves

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Abstract

Burgers-type equations are used to describe certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves is studied. Based on the Cole-Hopf transformation and a bilinear form, elastic-two-kink solutions are worked out, which can describe the elastic interaction between the two kink waves. Some complex conjugated transformations are obtained for us to construct the corresponding breather solutions. Via the breather solutions, multiple periodic solutions are derived. According to symbolic computation, hybrid solutions composed of the kink waves and breathers as well as half-/local-periodic kink solutions are seen. Moreover, the above solutions are graphically depicted for us to understand the influence of the coefficients and interaction of the waves: velocities and periods of all the aforementioned waves rely on the coefficients; except the breathers and one of the kink waves of the elastic-two-kink solutions, the waves are independent of the coefficients.

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Notes

  1. These breather solutions are different from those in Refs. [5, 6].

  2. These half-/local-periodic kink solutions can be reduced to the half-periodic kink solutions in Refs. [5, 6].

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11805020, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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

    Tian-Yu Zhou, Bo Tian & Yu-Qi Chen

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Zhou, TY., Tian, B. & Chen, YQ. Elastic Two-Kink, Breather, Multiple Periodic, Hybrid and Half-/Local-Periodic Kink Solutions of a Sharma-Tasso-Olver-Burgers Equation for the Nonlinear Dispersive Waves. Qual. Theory Dyn. Syst. 22, 34 (2023). https://doi.org/10.1007/s12346-022-00713-8

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