The main aim of this paper is to investigate the various dimensional nonlinear Fokas and Breaking soliton equations via a powerful analytical method, namely, sine-Gordon expansion method. Many new solutions such as complex combined dark-bright soliton solutions, singular and hyperbolic functions are derived. Choosing the suitable values of these parameters, various novel simulations are also plotted. Such results explain the wave behavior of the governing models, physically.

中文翻译：

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深入研究 (4 + 1) 维 Fokas 和 (2 + 1) 维断裂孤子方程

本文的主要目的是通过一种强大的解析方法，即正弦-戈登展开法，研究各种维度的非线性 Fokas 和 Breaking 孤子方程。导出了许多新的解，例如复组合的暗-亮孤子解、奇异函数和双曲函数。选择这些参数的合适值，还绘制了各种新颖的模拟。这样的结果在物理上解释了控制模型的波浪行为。