Exploring the optical soliton solutions of Heisenberg ferromagnet-type of Akbota equation arising in surface geometry by explicit approach

Faridi W.A. Bakar M.A. Riaz M.B. Myrzakulova Z. Myrzakulov R. Mostafa A.M.
June 2024 Springer

Optical and Quantum Electronics
2024 #56 Issue 6

This work tackles the Heisenberg ferromagnet-type integrable Akbota equation. The Akbota equation is significant model to visualize and study the surface geometry and curve analysis. The Akbota equation is an integrable coupled system of differential equations with soliton solutions. It is a crucial tool for researching nonlinear phenomena in differential geometry of curves and surfaces, magnetism, and optics. The generalized projective Riccati equation method, the Sardar sub-equation method, and the G^′G²-expansion method are the three separate analytical techniques used in this work. By using these approaches, exact analytical solutions for soliton waves are obtained, including dark, bright, singular, singular periodic, trigonometric, and hyperbolic waves. The creation of theoretical frameworks and the generalization of findings are made possible by analytical solutions. Researchers can frequently find patterns and relationships that apply more broadly by developing analytical solutions to particular cases, which results in the development of new theories and principles. The manuscript includes graphical representations, such as contour plots and two- or three-dimensional visualizations, in addition to theoretical derivations. These examples examine the propagation properties of the obtained soliton solutions and provide a promising basis for further research. Before this study, there is not existing any study in which, someone used these approaches and found solitons solutions.

Akbota equation (AE) , G^′G²-expansion method , Generalized projective Riccati equation method , Sardar Sub-equation method , Soliton solutions

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Department of Mathematics, University of Management and Technology, Lahore, Pakistan
IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, Kazakhstan
Department of Information Systems, College Computers and Information Science, King Saud University, Riyadh, Saudi Arabia

Department of Mathematics
IT4Innovations
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics
Department of Information Systems

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