In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

中文翻译：

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使用多重 exp 函数方法的非线性 burgers 方程的多重波解

在本文中，我们使用多重exp-function方法明确提出了行波解、双行波（DTW）解和三行波解（TW），包括单孤子、双孤子和三孤子解。对于非线性偏微分方程 (NPDE)，通过数学物理中的 (2+1) 维和 (3+1) 维非线性 Burgers PDE。在这项工作中，我们在 Maple 或 Mathematica 等计算机符号计算软件包的帮助下，成功地构建了一系列简单明了的新解决方案。我们将在某些情况下绘制一些图纸，并为每个获得的解决方案（例如单行波解决方案、双行波解决方案和 TWs）的相关参数提供特定值。这种方法在求解各类 NPDE 时非常有效且强大。