In this article, a generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system is investigated from the group standpoint. This system represents an interplay of long waves with distinct dispersion correlations. Using Lie’s theory several symmetry reductions are performed and the system is reduced to systems of non-linear ordinary differential equations (NLODEs). Subsequently, the simplest equation method is invoked to find exact solutions of the NLODE systems, which then provides the solitary wave solutions for the system under discussion. Finally, we construct conservation laws of generalized Hirota–Satsuma coupled KdV system with the aid of general multiplier approach.

中文翻译：

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广义Hirota-萨摩耦合流体力学KdV系统的闭式解和守恒律。

在本文中，从小组的角度研究了广义的Hirota-Satsuma耦合Korteweg-de Vries（KdV）系统。该系统代表具有明显色散相关性的长波相互作用。使用李理论，进行了几次对称约简，并将系统简化为非线性常微分方程（NLODE）的系统。随后，调用最简单的方程方法来找到NLODE系统的精确解，然后为正在讨论的系统提供孤立波解。最后，借助通用乘数法，构造了广义的广田-萨摩耦合KdV系统的守恒律。