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.
