Analysis of Generalized Boussinesq Coupled Equations Using Lie Symmetry

@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},
  }