Bifurcation analysis, chaos, and soliton solution of the temporal fractional NTME-II model in ferromagnetic spin systems

Abstract

In this research, we study the temporal fractional form of the Nurshuak-Tolkynay-Myrzakulov equation-II (NTME-II) model, focusing on bifurcation and chaos, and investigating advanced soliton solutions. The NTME-II equation has broad applications in various physical contexts, including nonlinear optics, ferromagnetic spin systems, and optical fiber communications. Initially, the bifurcation analysis is conducted to examine the dynamical behavior of the proposed system, revealing how parameter variations affect phase portraits and wave solutions, particularly illustrating transitions among periodic, solitary, and singular wave structures. The findings offer insights into the stability and evolution of nonlinear wave patterns. By adding an external force, we studied the system's chaotic behavior, including periodic, quasi-periodic, super-periodic, and chaotic regimes. Additionally, the soliton solution of the proposed model is investigated using the Modified Sardar Sub-equation (MSSE) approach. The attained solutions are presented as rational, trigonometric, exponential, and hyperbolic functions. The solutions include bright-type bell, double bell (dark-bright), dark-type bell, bright-type periodic wave, cross-periodic, and dark-type periodic waves, which are visualized through 3D, density, and 2D plots, and these are enhancing the solution space for these nonlinear evolution equations. The influence of temporal fraction is also presented through 2D and 3D plots.