In this article, we use the Sine–Cosine wavelets (SCWs) method to numerically solve the generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system. For this purpose, we use an approximation of functions with the help of SCWs, and we approximate spatial derivatives using this method. In this regard, to linearize the nonlinear terms of the equations, we use the quasilinearization technique. Also, the convergence analysis and the error estimation of the method are investigated. The operational matrix based on SCWs has a large number of zero components, which ensures good system performance and provides acceptable accuracy even with fewer collocation points. In the end, to show the efficiency and accuracy of the method in solving this system, a numerical example is provided and the results are compared with the Legendre wavelet (LW) method.

在本文中，我们使用 Sine-Cosine 小波 (SCW) 方法对广义 Hirota-Satsuma 耦合 Korteweg-de Vries (KdV) 系统进行数值求解。为此，我们在 SCW 的帮助下使用函数逼近，并使用这种方法逼近空间导数。在这方面，为了线性化方程的非线性项，我们使用准线性化技术。此外，还研究了该方法的收敛性分析和误差估计。基于 SCW 的运算矩阵具有大量的零分量，这确保了良好的系统性能，即使在搭配点较少的情况下也能提供可接受的精度。最后，为了说明该方法求解该系统的效率和准确性，提供了一个数值例子，并将结果与​​勒让德小波（LW）方法进行了比较。