Orateur : Olga Assainova (IMB)

Résumé

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. 

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