Modeling Wave Propagation with Gravity and Surface Tension: Soliton Solutions for the Generalized Hietarinta-Type Equation

Mostafa M.A. Khater

Ayuda

Modeling Wave Propagation with Gravity and Surface Tension: Soliton Solutions for the Generalized Hietarinta-Type Equation

Mostafa M. A. Khater ^[1]
1. [1] Xuzhou Medical University
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
Idioma: inglés
Enlaces
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Resumen
- This study explores analytical and approximate explicit solutions for the generalized Hietarinta-type equation, denoted as (GH), in the context of (2+1) dimensions. This investigation utilizes contemporary computational and numerical techniques, including the Khater II technique, He’s variational iteration method, and the septic–B–spline scheme. The GH equation serves as a mathematical representation of wave propagation on water surfaces, accounting for both gravity and surface tension effects. In fluid dynamics, different wavelengths of waves are associated with distinct phase velocities and frequencies. This research introduces innovative solitary wave solutions, visually depicted through figures, and rigorously assesses their computational accuracy using state-of-the-art numerical methods. The stability of these solutions is scrutinized through the characteristics of the Hamiltonian system. The solutions are reintroduced into the original GH model using Mathematica 13.1 software to validate the obtained results. This study holds significant importance in mathematical modeling and fluid dynamics because it explores the GH equation in (2+1) dimensions. The GH equation is a vital tool for modeling wave propagation on water surfaces, encompassing the interplay of gravity and surface tension, a phenomenon with broad practical applications. Additionally, the study contributes to the field by conducting a stability analysis of these solutions, providing insights into their dynamic behavior and long-term evolution.
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