Construction of traveling wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Abstract The present paper applies the exp ( − φ ( ξ ) ) -expansion and the extended tanh-function methods to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain (HFSC) equation. The applied methods acquire some new exact traveling wave solutions to the HFSC equation, which are representing the hyperbolic, trigonometric, exponential and rational function solutions. All solutions exhibit distinct physical configurations, such as the periodic, dark and singular soliton solutions. Three dimensional (3D) and two dimensional (2D) cross sectional graphics of some obtained solutions are confirmed the periodic, dark and singular behaviors. Furthermore, the conformable derivative is also considered and discussed for aforesaid methods to the HFSC equation. As outcomes, some new optical solutions are also attained in terms of fractionality. Obtained new solutions ensured that aforesaid methods are the reliable treatment for seeking nonlinear phenomena to HFSC equation as well as any NLEEs arising in mathematical physics and fiber optics.