In this article, some new traveling wave solutions to a (2+1)-dimensional version of the nonlinear Schrödinger equation are constructed through two analytical techniques. The main integration methods employed in this paper are the generalized exponential rational function method and the extended sinh–Gordon equation expansion method. These techniques enable us to integrate analytical solutions for the equation in many different structures. After finding solutions, a good description of the numerical behavior of obtained results in the form of several three-dimensional diagrams is also provided. One of the main advantages of employed methods is the relatively low cost and their straightforward structure compared to other existing techniques. Moreover, both methods determine analytical solutions of nonlinear models in terms of elementary functions. This distinctive feature enables us to employ them in solving other nonlinear problems as well. Necessary calculations in this article are done in symbolic form and within the framework of Maple software.

在本文中，通过两种分析技术构建了非线性薛定谔方程的 (2+1) 维版本的一些新行波解。本文采用的主要积分方法是广义指数有理函数法和扩展的sinh-Gordon方程展开法。这些技术使我们能够在许多不同的结构中整合方程的解析解。在找到解决方案后，还以几个三维图的形式很好地描述了所得结果的数值行为。与其他现有技术相比，所采用方法的主要优点之一是成本相对较低且结构简单。此外，这两种方法都根据初等函数确定非线性模型的解析解。这一独特的特征使我们也能够将它们用于解决其他非线性问题。本文中必要的计算均以符号形式并在 Maple 软件的框架内完成。