2025

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Closed form solitary wave solutions for the Jaulent-Miodek hierarchy model
(UMT Lahore, 2025-11-23) Kashif Shahzad
The jaulent-Miodek hierarchy system’s dynamical analysis is presented in this work. The jaulent-Miodek hierarchy equation incorporates an energy-dependent Schrödinger potential that finds use in fluid dynamics, condensed matter physics, engineering systems, and optics. Investigating this dynamic problem from a mathematical standpoint is therefore crucial. For the jaulent-Miodek model, the closed-form invariant solution known as solitons is investigated using the Sardar subequation approach. Under the noise, the various solitons are created as bright soliton, dark soliton, dark-bright soliton, periodic, and another form. It is seen that the model contains kink wave profiles, different soliton profiles, and periodic oscillating nonlinear waves. Some of the recently developed soliton solutions are validated by reintegrating them into the appropriate framework for soft computation using Wolfram Mathematica. By selecting appropriate parameter values, the various figures are plotted in both 2D and 3D along with the related contours.