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Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry
Subject area: Science,Engineering and Technology · Area of research: Mathematics
Abstract
In the last decades, Nonlinear partial differential equations (NPDEs) have become es- sential tools to model complex phenomena that arise in different aspects of science and engineering such as hydrodynamics. Therefore, constructing exact and approximate so- lutions of NLPDEs is of great importance in mathematical sciences. Previously authors have done similar work with restriction of K and L to be one. In this paper we solve the generalized Boussinesq coupled equations: ut + Kvx + Luux = 0; K > 0, L > 0 vt + uvx + uxxx = 0 using Lie symmetry of differential equations where u = u(x, t) is the velocity of water and v = v(x, t) the total depth of water and subscripts denote partial derivatives. The positive constants K,L would enable further analysis of optimal water depth and velocity be determined.
References
[1] Mohammed O. A. 2019. Solution of the coupled Boussinesq-Burger's equations by reduced differential transform method. ResearchGate.
[2] Shreekant P. P.,Twinkle S.2016.Solution of coupled non-linear system by optimal homotopy analysis method. ResearchGate.
[3] Anwar J. M. J.,Mahmood J.A.2018.Soliton Solutions of the Coupled Schrdinger-Boussinesq Equations for Kerr Law Nonlinearity. Hindawi.
[4] Hong-Qian S.,Ai-Hua C.2018.Exact solutions of the classical Boussinesq system. Taylor and Francis.
[5] Kamal R., Talaat S. EL-Danaf, Khalid A.2016.An efcient approach to numerical study of the coupled-bbm system with b-spline collocation method. Communication in Mathematical Modeling and Applications. CMMA 1, No. 3, 5-15 (2016)
[6] Oliver P., J. Applications of Lie Groups to Differential Equations,2nd ed. (1993). Springer-Verlag, Berlin.
How to cite this paper
@article{1702612,
author = {Sarah Omari, Vincent Marani, Michael Oduor},
title = {Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry},
journal = {Iconic Research And Engineering Journals},
year = {2021},
volume = {4},
number = {9},
pages = {1-5},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1702612.pdf},
abstract = {In the last decades, Nonlinear partial differential equations (NPDEs) have become es- sential tools to model complex phenomena that arise in different aspects of science and engineering such as hydrodynamics. Therefore, constructing exact and approximate so- lutions of NLPDEs is of great importance in mathematical sciences. Previously authors have done similar work with restriction of K and L to be one. In this paper we solve the generalized Boussinesq coupled equations:
ut + Kvx + Luux = 0; K > 0, L > 0
vt + uvx + uxxx = 0
using Lie symmetry of differential equations where u = u(x, t) is the velocity of water and v = v(x, t) the total depth of water and subscripts denote partial derivatives. The positive constants K,L would enable further analysis of optimal water depth and velocity be determined.},
month = {March},
}