Séminaire des doctorants

Student seminar

by Ms Olga Assainova (IMB)


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.