The aim of this study is to propose a combined numerical treatment for the dispersive partial differential equations involving dissipation, convection and reaction terms with nonlinearity, such as the KdV‐Burgers, KdV and dispersive‐Fisher equations. We use the combination of the exponential Rosenbrock–Euler time integrator and multiquadric‐radial basis function meshfree scheme in space as a qualitatively promising and computationally inexpensive method to efficiently exhibit behavior of such fruitful interactions resulting in antikink, two solitons and antikink‐breather waves. Obtained numerical solutions are compared with the existing results in the literature and discussed using illustrations in detail.

中文翻译：

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三阶色散偏微分方程的组合无网格指数Rosenbrock积分器

这项研究的目的是为包含耗散，对流和具有非线性的反应项的色散偏微分方程，例如KdV-Burgers，KdV和色散-Fisher方程，提出一个组合数值处理方法。我们将空间中的指数Rosenbrock-Euler时间积分器和多二次径向函数无网格方案结合使用，以作为定性有前途且计算成本低廉的方法来有效展示此类富有成果的相互作用的行为，从而产生反纽结，两个孤子和反纽结-喘息波。将获得的数值解与文献中的现有结果进行比较，并使用插图进行详细讨论。