University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 Optical solitons and stability analysis for the improved Eckhaus equations 690 700 19245 10.22034/cmde.2024.62793.2784 EN Hina Zulfiqar Department of Mathematics, Government Sadiq College Women University, Bahawalpur, Punjab 63100, Pakistan. Kalim U. Tariq 1. Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250 (AJK), Pakistan. \\ 2.Research Center of Applied Mathematics, Khazar University, Baku, AZ1096, Azerbaijan. Hamood Ur Rehman Department of Mathematics, University of Okara, Okara, Punjab 56300, Pakistan. Taiba Kouser Applied Research center of metrology and standard testing, King Fhad University of Petroleum and minerals Dhahran Saudi Arabia. Waqar Ahmad Department of Mathematics, University of Okara, Okara, Punjab 56300, Pakistan. Journal Article 2024 08 04 In this article, the propagation of modulated waves in one and two dimensional systems are analyzed 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 the nonlinear model are specified. These governing equations have some applications in domains like nonlinear optics, condensed matter physics and fluid dynamics. https://cmde.tabrizu.ac.ir/article_19245_ed1bc44e221162e8231f2a41d184181b.pdf