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  15.07.2014 - Integrable Equations in 3D: deformations of dispersionless limits - Seminario

 Mercoledi' 16 luglio, alle ore 16, presso l'aula Seminari, il Prof. V. Novikov, Loughborough University, terrà un seminario dal titolo:

Integrable Equations in 3D: deformations of dispersionless limits

Classification of integrable systems remains as a topic of active research from the beginning of soliton theory. Numerous classification results are obtained in 1 + 1 dimensions by means of
the symmetry approach. Although the symmetry approach is also applicable to 2 + 1-dimensional systems, one encounters additional difficulties due to the appearance of nonlocal variables. There are several techniques to tackle the problem (e.g. the perturbative symmetry approach). In the perturbative symmetry approach one starts with a linear equation having a degenerate dispersion law and reconstructs the allowed nonlinearity.In this talk we present a novel perturbative approach to the classification problem. Based on the method hydrodynamic reductions, we first classify integrable quasilinear systems which may potentially occur as dispersionless limits of integrable 2 + 1-dimensional soliton equations. Subsequently we construct dispersive deformations preserving integrability deforming the hyrdrodynamic reductions by dispersive deformations and requiring that all hydrodynamic reductions of the dispersionless limit will be inherited by the corresponding dispersive counterpart. The method also allows to effectively reconstruct Lax representations of the deformed systems. We present various classification results obtained in the frame of the new approach, e.g. the classification of scalar 2+1-dimensional equations generalizing KP, BKP/CKP, the classification of Davey-Stewartson type systems as well as various classifications of 2 + 1-dimensional differential-difference and fully discrete equations.

The talk is based on joint work with E. Ferapontov, A. Moro, B.
Huard and I. Roustemoglou.

Ref. Prof. R. Vitolo