The aim of this study is to find new exact solutions to the coupled Maccaris system by extended rational sine-cosine and rational sinh-cosh methods. By means of these methods, we found some fresh solitons of the above mentioned equation. The solutions are expressed in the form of new periodic,dark,bright and bright periodic solitons solutions. These methods are efficient, powerful, and they can be used as an alternative to establish new soliton of different types of differential PDEs applied in mathematical physics. Also, in order to visualize the underlying dynamics of the obtained soliton solutions, 2D and 3D plots are drawn. Computational results indicate not only the efficiency and strength of the methods but also further possible applicability potential of these techniques to some other significant nonlinear PDEs.

这项研究的目的是通过扩展有理正弦余弦和有理正弦余弦方法找到耦合Maccaris系统的新精确解。通过这些方法，我们发现了上述方程式的一些新鲜孤子。这些解决方案以新的周期，暗，亮和亮周期孤子解决方案的形式表示。这些方法高效，强大，可以用作建立数学物理中应用的不同类型微分PDE的新孤子的替代方法。同样，为了可视化获得的孤子解的基本动力学，绘制了2D和3D图。计算结果不仅表明了方法的效率和强度，而且还表明了这些技术对其他一些重要的非线性PDE的潜在应用潜力。