Analytical study of two nonlinear Schrödinger equations via optical soliton solutions

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 ([Formula: see text]-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.