In this study, we investigate two nonlinear Schrödinger equations (NLSEs) which point out the evolution of disturbances in dynamics. The first one is the nonlinear Heisenberg ferromagnetic spin chain equation of (2+1)-dimensional and the second one is (1+1)-dimensional cubic NLSE that govern the dynamics of modulated compressional dispersive Alfvén (CDA) envelope. The (G′/G)-expansion method is adopted to carry out this target in a straightforward way. A diversity of new hyperbolic and periodic solitary wave solutions are acquired. The obtained solutions with some constraint conditions show the validity and effectiveness of the method.

中文翻译：

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通过光孤子解对两个非线性薛定谔方程的解析研究

在这项研究中，我们研究了两个非线性薛定谔方程 (NLSE)，它们指出了动力学中扰动的演变。第一个是 (2+1) 维的非线性 Heisenberg 铁磁自旋链方程，第二个是 (1+1) 维三次 NLSE，它控制调制压缩色散 Alfvén (CDA) 包络的动力学。这 （G'/G)采用-expansion的方法，以一种直截了当的方式来实现这个目标。获得了多种新的双曲和周期性孤立波解。得到的具有一定约束条件的解表明了该方法的有效性和有效性。