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Here, different optical soliton wave solutions for a couple of nonlinear Schrödinger's equations (NLSEs), namely, the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) and the dynamics of modulated compressional dispersive alfven (CDA) are considered that describe the magnetic ordering in ferromagnetic materials and CDA waves produced in plasma physics. Hydromagnetics waves represent a key role to investigate electromagnetic disturbances in magnetized space. This equation is analysed utilizing one powerful integration tool, namely, the improved form offunction technique. It can be said that a couple of nonlinear Schrödinger's equations exist different dynamical behaviours. Finally, via symbolic computation, their dynamic structure and physical properties were vividly shown by two and three-dimensional plots and density plot.

Nonlinear spin dynamics of a couple of nonlinear Schrödinger's equations by the improved form of an analytical method