Paramasur, Nabendra.Shindin, Sergey Konstantinovich.Aluko, Olabisi Babatope.2023-11-072023-11-0720222022https://researchspace.ukzn.ac.za/handle/10413/22502Doctoral Degree, University of KwaZulu-Natal, Durban.The thesis contains a comprehensive theoretical and numerical study of the nonlinear Benjamin equation posed in the real line. We explore wellposedness of the problem in weighted settings and provide a detailed study of existence, regularity and orbital stability of traveling wave solutions. Further, we present a comprehensive study of the Malmquist-Takenaka-Christov (MTC) computational basis and employ it for the numerical treatment of the nonstaionary and the stationary Benjamin equations.enMalmquist-Takenaka-Christov Functions.Spectral collocation.Differential equations.Error bounds.Traveling waves.Thesis