Abstract:
In 1974 Davey and Stewartson used a multi-scale analysis to derive a coupled
system of nonlinear partial differential equations which describes the evolution of a
three dimensional wave packet in water of a finite depth. This system of equations
is the closest integrable two dimensional analog of the well-known one dimensional
nonlinear Schrodinger equation. The method of inverse scattering can thus be used
to solve the Davey-Stewartson equations in theory, but in practice this method is
not feasible with arbitrary initial conditions. In this thesis we present a numerical
method for solving the Davey-Stewartson equations. It is an extension of the split-step
Fourier method that proved to be so successful for the nonlinear Schrodinger
equation. This method is tested on some known soliton and dromion solutions and
then used to study modulational instability and solutions which become singular in
finite time.
