In this research article, the authors investigate the interaction of solitary waves for complex modified Korteweg–de Vries (CMKdV) equations using Chebyshev pseudospectral methods. The proposed method is established in both time and space to approximate the solutions and to prove the stability analysis for the equations. The derivative matrices are defined at Chebyshev–Gauss–Lobbato points and the problem is reduced to a diagonally block system of coupled nonlinear equations. For numerical experiments, the method is tested on a number of different examples to study the behavior of interaction of two and more than two solitary waves, single solitary wave at different amplitude parameters and different polarization angles. Numerical results support the theoretical results. A comprehensive comparison of numerical results with the exact solutions and other numerical methods are presented. The rate of convergence of the proposed method is obtained up to seventh‐order.

中文翻译：

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用Chebyshev伪谱方法对复杂修正Korteweg-de Vries方程孤立波的数值解和稳定性分析。

在本文中，作者使用Chebyshev伪谱方法研究了复杂修正Korteweg-de Vries（CMKdV）方程的孤波相互作用。建立了该方法在时间和空间上的近似解，并证明了方程的稳定性。导数矩阵在Chebyshev–Gauss–Lobbato点处定义，问题被简化为耦合非线性方程的对角线块系统。对于数值实验，该方法在多个不同的示例上进行了测试，以研究两个和两个以上孤立波，单个孤立波在不同振幅参数和不同偏振角下的相互作用行为。数值结果支持理论结果。给出了数值结果与精确解和其他数值方法的全面比较。所提出方法的收敛速度可达到七阶。