This paper studies novel analytical solutions of the extended (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation which is also known with (2 + 1)-dimensional complex Fokas ((2 + 1)D–CF) system. Fokas derived this system in 1994 by using the inverse spectral method. This model is considered as an icon model for nonlinear pulse propagation in monomode optical fibers. Many novel computational solutions are constructed through two recent analytical schemes (Ansatz and Projective Riccati expansion (PRE) methods). These solutions are represented through sketches in 2D, 3D, and contour plots to demonstrate the dynamical behavior of pulse propagation in breather, rogue, periodic, lump, and solitary characteristics. The stability property of the obtained solutions is examined based on the Hamiltonian system’s properties. The obtained solutions are checked by putting them back into the original equation through Mathematica 12 software.

中文翻译：

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Fokas系统的分析模拟；扩展 (2 + 1) 维非线性薛定谔方程

本文研究了扩展的新解析解(2 + 1)维非线性薛定谔 (NLS) 方程，也称为(2 + 1)维复数 Fokas ((2 + 1)D-CF) 系统。Fokas 在 1994 年通过使用逆谱法推导出了这个系统。该模型被认为是单模光纤中非线性脉冲传播的图标模型。许多新颖的计算解决方案是通过两种最近的分析方案（Ansatz 和 Projective Riccati 展开 (PRE) 方法）构建的。这些解决方案通过 2D、3D 和等高线图的草图来表示，以展示脉冲传播在呼吸、流氓、周期性、集中和孤立特征中的动态行为。基于哈密顿系统的性质检查获得的解决方案的稳定性。得到的解通过 Mathematica 12 软件将它们放回原始方程来检查。