Analyzing Sensitivity and Solitonic Behavior Using the Dullin-Gottwald-Holm Model in Shallow Water Waves
Journal Title: Acadlore Transactions on Applied Mathematics and Statistics - Year 2023, Vol 1, Issue 2
Abstract
This paper presents an investigation of traveling wave solutions and a sensitivity analysis for the unidirectional Dullin-Gottwald-Holm (DGH) system, a well-established model for wave propagation in shallow water. We apply the novel auxiliary equation method, a unique integration norm, to extract various soliton solutions, including kink, rational, bright, singular, and bright-singular solutions. Precise explicit solutions of the resultant ordinary differential equations are demonstrated using suitable parametric values. Furthermore, we explore the conditions that ensure the existence of these solutions. By applying the Galilean transformation, we convert the model into a planar dynamical system and evaluate its sensitivity performance. The selection of appropriate parameters enables the generation of two and three-dimensional sketches, as well as contour plots for each solution.
Authors and Affiliations
Shaheera Haroon, Muhammad Abuzar, Muhammad Faisal Khan
Keywords
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- EP ID EP732903
- DOI 10.56578/atams010205
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