Nonlinear long waves in shallow water for normalized Boussinesq equations

In this work, we investigate a partial differential equation (PDE) derived from a Boussinesq system of two equations that describe the wave motion in shallow water when the wavelength is small compared to wave amplitude. The Lie point symmetries of the PDE are utilized to reduce it to an ordinary di...

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Bibliographic Details
Published in:Results in Physics
Main Authors: Mosito Lekhooana, Motlatsi Molati
Format: Article
Language:English
Published: Elsevier 2024-04-01
Subjects:
Shallow water
Solitary waves
Boussinesq equations
Lie symmetry analysis
Travelling wave solutions
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379724002973
Description
Summary:In this work, we investigate a partial differential equation (PDE) derived from a Boussinesq system of two equations that describe the wave motion in shallow water when the wavelength is small compared to wave amplitude. The Lie point symmetries of the PDE are utilized to reduce it to an ordinary differential equation (ODE) the travelling wave solutions of which are obtained. These solutions are of trigonometric, hyperbolic and exponential types. Graphical representation of some solutions exhibiting solitary and cnoidal wave phenomena are presented.
ISSN:2211-3797

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