Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

M F Uddin; M G Hafez; S A Iqbal

doi:10.1016/j.heliyon.2022.e09199

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

Heliyon. 2022 Mar 24;8(3):e09199. doi: 10.1016/j.heliyon.2022.e09199. eCollection 2022 Mar.

Authors

M F Uddin¹, M G Hafez¹, S A Iqbal^{1

2}

Affiliations

¹ Department of Mathematics, Chittagong University of Engineering and Technology, Chattogram-4349, Bangladesh.
² Department of Electrical and Electronic Engineering, International Islamic University Chittagong, Chattogram 4225, Bangladesh.

Abstract

The oblique plane waves with their dynamical behaviors for a (2+1)-dimensional nonlinear Schrödinger equation (NLSE) having beta derivative spatial-temporal evolution are investigated. In order to study such phenomena, NLSE is converted to a nonlinear ordinary differential equation with a planar dynamical system by considering the variable wave transform with obliqueness and the properties of the beta derivative. Some more new general forms of analytical solutions, like bright, dark, singular, and pure periodic solutions of NLSE are constructed by employing the auxiliary ordinary differential equation method and the extended simplest equation method. The effect of obliqueness and beta derivative parameter on several types of wave structures along with the phase portrait diagrams are reported by considering some special values of parameters for the existence of attained solutions. It is found that the planar dynamical system is not supported by any type of orbit for $Θ = 45^{0}$ . It is also confirmed from the obtained solutions that no plane waves are generated for $Θ = 45^{0}$ . The presented studies on bifurcation analysis and analytical solutions for (2+1)-dimensional NLSE would be very useful to understand the physical scenarios of nonlinear spin dynamics in magnetic materials for Heisenberg models of ferromagnetic spin chains.

Keywords: AODEM; Beta fractional spatial-temporal NLSE; Bifurcation analysis; ESEM; Oblique plane wave phenomena.