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.