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Optical solitons and stability analysis for the improved Eckhaus equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 بهمن 1403 اصل مقاله (4.58 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.62793.2784 | ||
| نویسندگان | ||
| Hina Zulfiqar1؛ Kalim U. Tariq* 2؛ Hamood Ur Rehman3؛ Taiba Kouser4؛ Waqar Ahmad3 | ||
| 1Government Sadiq College Women University, Bahawalpur, Punjab 63100, Pakistan. | ||
| 2Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250 (AJK), Pakistan. | ||
| 3Department of Mathematics, University of Okara, Okara, Punjab 56300, Pakistan. | ||
| 4Applied Research center of metrology and standard testing, King Fhad University of Petroleum and minerals Dhahran Saudi Arabia. | ||
| چکیده | ||
| In this article, the propagation of modulated waves in one and two dimensional systems are analysed by investigating the improved Eckhaus models analytically. Along with additional dimensions, dissipative factors, nonlocal effects, and higher-order nonlinear elements, the enhanced Eckhaus equation expands the original Eckhaus equation. The investigation of the governing models' optical soliton solutions, including periodic, dark, brilliant, and singular solitons, is the focus of this article. This is done by obtaining a novel optical solution using the tanh-coth approach. Another type that incorporates nonlinearity and modulation effects in both spatial dimensions, and includes an extra spatial dimension, is the $(2+1)$-dimensional enhanced Eckhaus model. These equations are effective resources for examining a wide range of one- and two-dimensional system physical phenomena, including pattern generation, wave interaction, and soliton dynamics. Analyzing these equations can be challenging due to their higher dimensionality and nonlinear nature and numerical methods are often used to obtain solutions for specific cases or conditions. Consequently, trigonometric function solutions, hyperbolic function output and exponential functions solution with Independent parameters are acquired.3D and 2D contour plots of some solutions of nonlinear model are specified. These governing equations have some applications in domains like nonlinear optics, condensed matter physics and fluid dynamics. | ||
| کلیدواژه‌ها | ||
| The improved Eckhaus model؛ optical solitons؛ exact solutions؛ stability analysis؛ nonlinear dynamics | ||
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