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.