Document Type : Research Paper
Authors
1
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt.
2
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, El Shorouk City, Cairo, Egypt.
3
Department of Mathematics, Faculty of Basic Sciences, The German University in Cairo (GUC), Cairo, Egypt.
4
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Abstract
The stochastic Heisenberg ferromagnetic spin chain equation (SHFSCE) is a fundamental part of modern magnetism theory. The long-range ferromagnetic ordering magnetism with nonlinearity was explained by SHFSCE. It also shows the magnetism of various insulating crystals and interaction spins. Furthermore, ferromagnetism is fundamental to modern industry and technology and serves as the foundation for a number of electrical and electro-mechanical devices, such as generators, electric motors, and electromagnets. In this work, the nonlinear (2+1)-dimensional HFSCE is effectively solved using the improved modified extended (IME) tanh function technique, and its exact solutions are examined. We therefore give several new precise solutions, such as Jacobi elliptic functions (JEFs), (bright, singular, dark) soliton, rational solution, singular periodic solution, Weierstrass elliptic doubly periodic type solutions, and exponential solutions. These new solutions have never been reported before in the models studied. Single solitons that have never been seen before are the novel answers for the research models. Furthermore, the discovered solutions are used to create a number of fascinating 2D and 3D figures. The geometrical representation of the SHFSCE provides the dynamical information required to describe the physical phenomena. The results are crucial for understanding and studying the (2+1)-dimensional SHFSCE. In order to find distinct soliton solutions and other accurate solutions for various kinds of nonlinear differential equations (NLDEs), more studies on the IME tanh function technique may help. This discovery represents a significant breakthrough in our understanding of the complex and unpredictable behavior of this mathematical model.
Keywords
Main Subjects
)