Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry

• Author(s): Sarah Omari ; Vincent Marani ; Michael Oduor
• Paper ID: 1702612
• Page: 1-5
• Published Date: 03-03-2021
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 4 Issue 9 March-2021

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.

Citations

IRE Journals:
Sarah Omari , Vincent Marani , Michael Oduor "Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry" Iconic Research And Engineering Journals Volume 4 Issue 9 2021 Page 1-5

IEEE:
Sarah Omari , Vincent Marani , Michael Oduor "Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry" Iconic Research And Engineering Journals, 4(9)