In this paper, abundant exact wave solutions of fourth-order Ablowitz–Kaup–Newell–Segur water wave (AKNS) equation have been investigated by using the innovative and efficient method called improved $tanh(\frac{\phi (\xi )}{2})$-expansion method (IThEM). The obtained solutions for AKNS equation are in the form of hyperbolic, trigonometric, exponential, logarithmic functions that are completely new and distant from previously derived solutions. To have the knowledge of dynamical physical characteristics of this equation, some important solutions have been discussed graphically in the form of two and three-dimensional along with contour plots by selecting suitable parameters with the aid of Maple program. The achieved outcomes exhibit that this new method is efficient, direct, and provides different classes of families. This technique can solve many nonlinear differential equations having importance in different field of sciences.

在本文中，通过使用称为改进的创新和有效的方法，研究了四阶 Ablowitz–Kaup–Newell–Segur 水波 (AKNS) 方程的丰富精确波解$tanh(\frac{\phi (\xi )}{\mathrm{2个}})$-扩展方法（IThEM）。获得的 AKNS 方程解的形式为双曲函数、三角函数、指数函数和对数函数，这些函数是全新的，与以前导出的解有很大的不同。为了了解该方程的动态物理特性，通过借助 Maple 程序选择合适的参数，以二维和三维形式以及等高线图以图形方式讨论了一些重要的解。取得的成果表明，这种新方法高效、直接，并提供不同类别的家庭。该技术可以解决许多在不同科学领域具有重要意义的非线性微分方程。