Abundant Exact Soliton Solutions of the ( 2 + 1 )-Dimensional Heisenberg Ferromagnetic Spin Chain Equation Based on the Jacobi Elliptic Function Ideas

Abstract

The Heisenberg ferromagnetic spin chain equation (HFSCE) is very important in modern magnetism theory. HFSCE expounded the nonlinear long-range ferromagnetic ordering magnetism. Also, it depicts the characteristic of magnetism to many insulating crystals as well as interaction spins. Moreover, the ferromagnetism plays a fundamental role in modern technology and industry and it is principal for many electrical and electromechanical devices such as generators, electric motors, and electromagnets. In this article, the exact solutions of the nonlinear ( $2+1$ )-dimensional HFSCE are successfully examined by an extended modified version of the Jacobi elliptic expansion method (EMVJEEM). Consequently, much more new Jacobi elliptic traveling wave solutions are found. These new solutions have not yet been reported in the studied models. For the study models, the new solutions are singular solitons not yet observed. Additionally, certain interesting 3D and 2D figures are performed on the obtained solutions. The geometrical representation of the HFSCE provides the dynamical information to explain the physical phenomena. The results will be significant to understand and study the ( $2+1$ )-dimensional HFSCE. Therefore, further studying EMVJEEM may help researchers to seek for more soliton solutions to other nonlinear differential equations.