In this article, we construct multi-wave, homoclinic breather, M-shaped rational and periodic cross kink wave solutions for coupled-Higgs equation (CHE) by using distinct transformations. We obtain these solutions with the aid of logarithmic transformations and symbolic computations. Moreover, we also derive some soliton wave solutions for CHE in polynomial forms. These solutions include solitary wave, soliton wave and Jacobi elliptic function solutions and are found by implementing unified technique. We will also discuss the graphical structure of our newly achieved results.

中文翻译：

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耦合希格斯方程的多波、同宿呼吸器、M型有理等孤波解

在本文中，我们通过使用不同的变换构造了耦合希格斯方程 (CHE) 的多波、同宿呼吸器、M形有理和周期交叉扭结波解。我们借助对数变换和符号计算来获得这些解。此外，我们还推导出多项式形式的 CHE 孤子波解。这些解包括孤波、孤子波和雅可比椭圆函数解，是通过实施统一技术找到的。我们还将讨论我们新取得的成果的图形结构。