This paper studies the new closed form solutions to (2+1)-dimensional Bogoyavlenskii system that describes interaction of a Riemann wave propagation. The extended Fan sub-equation technique is used to investigate some new traveling wave solutions to the higher-dimensional coupled model. The obtained closed form solutions are named as shock, kink, shock and periodic soliton solutions. Clearly, the outcomes of the study confirm the strength of the current approach. Moreover, the obtained results are helpful for the understanding of non-linear wave propagation and are of great interest to present-day scientists and can be employed to deal with more complex models arising in diverse disciplines of contemporary science.

中文翻译：

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关于新的封闭形式解决方案：（2+1）维 Bogoyavlenskii 系统

本文研究了描述黎曼波传播相互作用的 (2+1) 维 Bogoyavlenskii 系统的新封闭形式解。扩展范子方程技术用于研究高维耦合模型的一些新的行波解。得到的闭式解称为激波解、扭结解、激波解和周期孤子解。显然，研究结果证实了当前方法的强度。此外，所获得的结果有助于理解非线性波传播，并且对当今的科学家非常感兴趣，并且可以用于处理当代科学不同学科中出现的更复杂的模型。