Exponential integrators for the investigation of stability of nonlinear waves

One important mechanism for the generation of nonlinear internal waves is the interaction of tides with topography. A model of this process is the forced Gardner equation. In this thesis efficient numerical methods are proposed to investigate this equation where the topography is much longer than the characteristic wavelength, which is a computationally difficult problem. The forced Gardner equation is then investigated. Significant phase changes in the behaviour of the nonlinear waves are identified and explained, and the types of resonant solutions are documented as the topographic amplitude and flow speed are varied, including solutions previously unknown for this equation.