Abstract

In this research, we delve into the exploration of the Kuralay-IIA equation by employing two power full approaches, namely extended hyperbolic function method (EHFM) and the improved modified Sardar-subequation method (IMSSEM). Applications of the Kuralay-IIA equation can be observed in a variety of physical phenomena, particularly in optical fibers, magnetic materials, and nonlinear optics. This equation performs an essential part in understanding gas behavior. Specifically, it offers an image of the relationship between volume, temperature and pressure in a gas system. We proceed through the matter in detail through the use of space curves which demonstrate integrable motion. Using the proposed techniques, our investigation provides an extensive variety of soliton solutions, such as periodic, dark–bright, bright, dark, solitary, and some other solutions. These solutions are in good alignment with previous study findings in this area. Analytical wave solutions are vital as they provide a basic comprehension of the physics or mathematics at play and establish a framework for further studies. The findings obtained from this study may help design models to come. The techniques used in this study are very effective, straightforward, and capable of handling more nonlinear models with high reliability. We use the Mathematica software to validate the accuracy and reliability of our results. Using carefully constructed 2D and 3D graphs generated, the resulting solutions are visually shown.

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