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Dark and singular solitons to the two nonlinear Schrödinger equations
In this study, we investigate two nonlinear Schrödinger equations which describe the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains (HFSC) with bilinear and anisotropic interactions in the semiclassical limit and the dynamics of modulated compressional dispersive Alfvén (CDA) waves arising in plasma physics, respectively by using the modified extended tanh expansion method with Riccati differential equation. Dark, singular, combined dark-singular soliton, singular periodic waves and rational function solutions are successfully constructed to the two studied nonlinear models. We give the constraint conditions that validate the existence of the reported soliton solutions. The 2D, 3D, and the contour graphs to some of the obtained solutions are plotted.