Uddin M F, Hafez M G, Iqbal S A
Department of Mathematics, Chittagong University of Engineering and Technology, Chattogram-4349, Bangladesh.
Department of Electrical and Electronic Engineering, International Islamic University Chittagong, Chattogram 4225, Bangladesh.
Heliyon. 2022 Mar 24;8(3):e09199. doi: 10.1016/j.heliyon.2022.e09199. eCollection 2022 Mar.
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 . It is also confirmed from the obtained solutions that no plane waves are generated for . 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.
研究了具有β导数时空演化的(2 + 1)维非线性薛定谔方程（NLSE）的斜平面波及其动力学行为。为了研究此类现象，通过考虑具有倾斜度的变量波变换和β导数的性质，将NLSE转换为具有平面动力系统的非线性常微分方程。利用辅助常微分方程方法和扩展的最简方程方法，构造了NLSE的一些更新的一般形式的解析解，如亮孤子解、暗孤子解、奇异解和纯周期解。通过考虑所得到解存在的参数的一些特殊值，报告了倾斜度和β导数参数对几种类型波结构的影响以及相图。发现对于 ，平面动力系统不被任何类型的轨道所支持。从所得到的解中还证实，对于 不产生平面波。所提出的关于(2 + 1)维NLSE的分岔分析和解析解的研究对于理解铁磁自旋链海森堡模型中磁性材料非线性自旋动力学的物理场景将非常有用。
