Zhu He, Manafian Jalil, Hammadi Alaa Hussein, Ilhan Onur Alp, Lakestani Mehrdad, Malmir Somaye, Mahmoud K H
Software Engineering Institute of Guangzhou, Guangzhou, Guangzhou, 510990, China.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Sci Rep. 2025 Jul 1;15(1):21649. doi: 10.1038/s41598-025-03483-w.
This paper devote to investigate plenteous optical and other soliton solutions to the generalized nonlinear Schrödinger equation with the parabolic nonlinear (NL) law by employing two analytical techniques. The analytical schemes are the improved function strategy and the combined - function strategy. Different sets of exponential function solutions are reached. Two reliable integration standards are locked in to devise optical dark, singular, combo, complex and periodic solutions. The detailed solutions contain key applications in building and material science. These solutions characterize the wave execution of the overseeing models, really. By the choice of reasonable parametric values, the flow of the assessed comes about by portraying their 2D, 3D and density profiles to get it the genuine phenomena for such sort of nonlinear models. The main point of this investigation is that one can visualize and overhaul the knowledge to overcome the foremost common strategies and to illuminate the ODEs and PDEs. The novel conservation law theorem is investigated. On evaluating the Chupin Liu's theorem for the grey and black solitons, to the grey and black optical solitons, the new sets of combined optical soliton solutions of the model are constructed. It is illustrated that these solutions approved the program utilizing Maple and found them adjusted. The suggested strategies for settling NLPDEs have been planned to be useful, simple, convenient, and sensible. At long last, the presence of the solutions for the imperative conditions is additionally appeared.
本文致力于通过运用两种分析技术，研究具有抛物线型非线性（NL）定律的广义非线性薛定谔方程的大量光学孤子解和其他孤子解。分析方案为改进的函数法和组合函数法。得到了不同组的指数函数解。采用两种可靠的积分准则来设计光学暗孤子、奇异孤子、组合孤子、复孤子和周期孤子解。详细的解在建筑和材料科学中有重要应用。实际上，这些解表征了主导模型的波动行为。通过选择合理的参数值，通过描绘它们的二维、三维和密度分布来评估结果的流动情况，以了解此类非线性模型的真实现象。本研究的重点在于，可以可视化并更新知识，以克服最常见的策略，并阐明常微分方程和偏微分方程。研究了新的守恒律定理。在将丘平·刘定理应用于灰色和黑色孤子，进而应用于灰色和黑色光学孤子时，构建了该模型的新的组合光学孤子解组。结果表明，这些解通过Maple程序验证，并且发现它们是合适的。所提出的求解非线性偏微分方程的策略已被设计为有用、简单、方便且合理的。最后，还展示了在强制条件下解的存在性。
