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Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients

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Abstract

In this article, the bilinear form, Bäcklund transformation, Lax pair and infinite conservation laws of the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients are constructed based on the Bell polynomials approach. N-soliton solutions are studied by means of introducing the complex conjugate condition technique and selecting appropriate test functions and parameters, including the hybrid solution of the a-order kink waves, b-order periodic-kink waves and c-order periodic-breather waves. The homoclinic test method is applied to investigate their dynamical interaction properties between different forms of hybrid-type solutions. Besides, a number of examples are presented by choosing different types of interactions among the hybrid-type solutions. Finally, we analyze the wave propagation direction and velocity to reflect the novel evolutionary behaviors in the three-dimensional profile of the model. These results are helpful to the study of local wave interactions in nonlinear mathematical physics.

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Acknowledgements

The authors deeply appreciate the anonymous reviewers for their helpful and constructive suggestions, which can help improve this paper further. This work has been supported by the National Natural Science Foundation of China (Grant No. 11361040), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2020LH01008), the Graduate Students’ Scientific Research Innovation Fund Program of Inner Mongolia Normal University, China (Grant No. CXJJS19096, No. CXJJS20089) and the Graduate Research Innovation Project of Inner Mongolia Autonomous Region, China (Grant No. S20191235Z).

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Han, PF., Bao, T. Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients. Nonlinear Dyn 107, 1163–1177 (2022). https://doi.org/10.1007/s11071-021-07019-5

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