Description

__ Title:__ On the semiclassical limit of the defocusing Davey-Stewartson II equation

Inverse scattering is the most powerful tool in theory of integrable systems. Starting in the

late sixties resounding great progress was made in (1+1) dimensional problems with many

break-through results as on soliton interactions. Naturally the attention in recent years turns

towards higher dimensional problems as the Davey-Stewartson equations, an integrable

generalisation of the (1 + 1)-dimensional cubic nonlinear Schrödinger equation. Here we will

consider the direct spectral transform for the defocusing Davey-Stewartson II equation for

smooth initial data in the semi-classical limit, which is well known in quantum mechanics.

Particularly, it will be shown how the direct spectral transform involves a singularly

perturbed elliptic Dirac system in two dimensions that can be solved in certain cases by the WKB-tyme method.

Finally, we will present the appropriate numerical study that supports the rigorous semiclassical analysis of this problem.

Finally, we will present the appropriate numerical study that supports the rigorous semiclassical analysis of this problem.