In this study, we investigate the nonlinear Zoomeron equation by using the extended rational sin − cos and sinh − cosh methods. We successfully constructed some important solutions such as singular periodic wave, periodic wave, topological, and singular soliton solutions. Using suitable parameter values, we present the numerical simulations to some of the obtained results via the 2- and 3-dimensional graphs. The methods used in this study are efficient and powerful mathematical tools that can be applied in reporting various wave solutions to different nonlinear physical models.

中文翻译：

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Zoomeron方程的扩展有理sin-cos和sinh-cosh方法解析解

在这项研究中，我们使用扩展的有理 sin - cos 和 sinh - cosh 方法研究非线性 Zoomeron 方程。我们成功地构建了一些重要的解，如奇异周期波、周期波、拓扑和奇异孤子解。使用合适的参数值，我们通过 2 维和 3 维图对获得的一些结果进行数值模拟。本研究中使用的方法是有效且强大的数学工具，可用于报告不同非线性物理模型的各种波解。