In this paper, we investigate a diverse collection of exact solutions to a version of nonlinear Schrödinger equation with Kerr law nonlinearity. These results are obtained for the equation using the generalized exponential rational function method. The graphical interpretation of the solutions is also included to demonstrate the dynamic characteristics of the achieved results. It is found that the proposed methodology is not only very simple, straightforward but also efficient and powerful. This technique discovers very diverse categories of solutions in a single framework. This feature is one of the main advantages of this method. By taking the appropriate values of existing parameters in solutions, several numerical simulations have been presented. Moreover, it can also be adopted on solving other nonlinear models in mathematical physics. The use of the paper’s method is also suggested in solving other partial equations. All symbolic calculations in this article are performed using Mathematica software.

在本文中，我们研究了具有克尔定律非线性的非线性薛定谔方程版本的精确解的不同集合。这些结果是使用广义指数有理函数方法为方程获得的。还包括解决方案的图形解释，以展示所取得结果的动态特性。发现所提出的方法不仅非常简单、直接而且高效和强大。这种技术在单个框架中发现了非常多样化的解决方案类别。此功能是此方法的主要优点之一。通过取解中现有参数的适当值，已经提出了几种数值模拟。此外，它还可以用于求解数学物理中的其他非线性模型。还建议在求解其他偏方程时使用本文的方法。本文中的所有符号计算均使用 Mathematica 软件进行。