Soliton Solutions of (2 + 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine- cosine and sinh- cosh Method


ÇINAR M. , ÖNDER İ. , SEÇER A. , Yusuf A., Sulaiman T. A. , Bayram M., ...More

International Journal of Applied and Computational Mathematics, vol.7, no.4, 2021 (Refereed Journals of Other Institutions) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s40819-021-01076-5
  • Title of Journal : International Journal of Applied and Computational Mathematics
  • Keywords: (2 + 1) dimensional Heisenberg equation, Analytical method, Nonlinear PDE, sin - cos method, sinh - cosh method, Solitons

Abstract

© 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.In this research, our main motivation is to find the novel analytical solutions of (2 + 1) dimensional Heisenberg ferromagnetic spin equation, which describes the nonlinear dynamics of the ferromagnetic materials by using the extended rational sine- cosine and sinh- cosh methods. The considered PDE is converted to an ODE by applying a wave transformation, and then the solutions of the ODE are supposed to be in the rational forms of trigonometric functions. After substituting the solutions to the ODE and doing some basic calculations, a system of algebraic equations is derived. So, finding the solutions of the PDE turns into a problem of solving an algebraic system of equations. The unknown coefficients in the solutions that are in the rational form are found by solving the obtained system. The methods are powerful and can be applied to find exact solutions to lots of PDEs in mathematical physics.