Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

The Myrzakulov–Lakshmanan Equation-II (MLE-II) that refers to the (2 + 1)-dimensional integrable spin system has five various formalisms. In Our current study we will construct new types of the soliton solutions for only one of these forms namely the MLE-II. These new types of soliton solutions will be constructed through three impressive, effective methods that are employed for the first time to this model. These three methods are the generalized Kudryashov method (GKM), the (G'/G)-expansion method and the differential transform method (DTM). The first two methods are applied to extract the soliton solutions of the suggested model while the third one whose initial conditions emerged from the achieved soliton solutions is considered one of famous numerical methods that we will use to obtain the identical numerical solutions for the realized soliton solutions to ensure quality of these soltions. Moreover, we will establish the 2D, 3D plot simulations to show the characteristic for the dynamic of the newly achieved soliton solutions.