Analysis of nonlinear Benjamin equation posed on the real line.

Abstract

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.