Liu Yuanyuan, Manafian Jalil, Singh Gurpreet, Alkader Naief Alabed, Nisar Kottakkaran Sooppy
Department of Mathematics and Artificial Intelligence, Lyuliang University, Lüliang, China.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Sci Rep. 2024 Mar 15;14(1):6317. doi: 10.1038/s41598-024-56719-6.
This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail.
本文主要致力于运用广义G展开法获取解及其他精确行波解。利用该方法提取了耦合非线性薛定谔系统的一些新的精确解。此方法基于扩展法非线性模型的一般性质，并借助多项式方法的完全判别系统以及诸如Maple或Mathematica等计算机代数系统（AS）。研究了双折射光波导中具有超宽非傍轴脉冲传播的非傍轴孤子。为此，给出了耦合非线性亥姆霍兹（CNLH）系统的一个示例，以说明本研究中所采用策略的可行性和稳定性。这些解对于理解克尔介质、光学计算以及克尔类非线性介质中的光束时波导的行为具有重要意义。通过二维和三维的各种图形以及密度图对解的物理意义进行了模拟。还详细报道了解存在的约束条件。最后，详细给出了CNLH方程的调制不稳定性分析。
