ORIGINAL RESEARCH article
Front. Phys.
Sec. Statistical and Computational Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1637491
Soliton Dynamics and Stability in the Boussinesq Equation for Shallow Water Applications
Provisionally accepted
- 1University of the Punjab, Lahore, Pakistan
- 2Imam Muhammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
- 3Chengdu University, Chengdu, China
Select one of your emails
You have multiple emails registered with Frontiers:
Notify me on publication
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
This manuscript deals with the Fourth-order Boussinesq water wave equation, which is integrable and possesses soliton solutions. Boussinesq water wave equation is a vital tool for investigating nonlinear phenomena in various waves and shallow water phenomena in fluid dynamics, such as diffraction, refraction, weak nonlinearity, and shoaling. Along with fluid dynamics, it is essential in many disciplines of physics, including the transmission of long waves in shallow waters, vibrations in a nonlinear string, acoustics, laser optics, and one-dimensional nonlinear lattice waves. The Generalized Arnous approach, the new Kudryashov method, and the Modified Sub-equation method are applied to this objective. The resultant diverse solutions consist of trigonometric and hyperbolic functions. These approaches generate accurate analytical curves for soliton waves, which comprise kink, bright, and dark waves. The graphical aspects of the produced solutions are investigated using $3D$-surface graphs, $2D$-line graphs, and contour and polar plots, in addition to theoretical derivations. This work is novel in its integrated use of three symbolic methods to derive a broad spectrum of exact soliton solutions for the fourth-order Integrated Boussinesq water wave equation, including compound and hybrid waveforms. The inclusion of the graphical visualization, stability analysis, and open source code resources further strengthens its contribution to nonlinear wave modeling.
Keywords: Fourth-order boussinesq water wave equation, modified sub-equation method, New Kudryashov method, Riccati equation method, Solitary wave solutions
Received: 29 May 2025; Accepted: 04 Aug 2025.
Copyright: © 2025 Farooq, Alshammari, Li and Hussain. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Zhao Li, Chengdu University, Chengdu, China
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.