In the current paper, a review of the Homotopy perturbation method is offered thoroughly to fetch the analytical solution of coupled 1D non-linear Burgers’ equation. The exact solution of the coupled 1D Burgers’ equation is attained in the system of a power series, (convergent in nature). A suitable optimal of the initial condition leads towards the vital exact solution after some iterative phases.

中文翻译：

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用同伦摄动法（HPM）耦合一维非线性Burgers方程的精确解：综述

在本文中，对同伦摄动法进行了全面的综述，以获取耦合的一维非线性Burgers方程的解析解。在幂级数系统（本质上是收敛的）中可以获得耦合的1D Burgers方程的精确解。在某些迭代阶段之后，适当的最佳初始条件将导致至关重要的精确解。