Classification of integrable systems in 2D:deformation of dispersionless systems

Abstract:

The following approach to the classification integrable systems in 2+1 D will be discussed:

1. First of all, one classifies dispersionless integrable systems based on the method of hydrodynamic reductions;

2. Secondly, one constructs their dispersive deformations based on the requirement that the dispersive system inherits deformations of all hydrodynamic reductions of its dispersionless limit.

Examples illustrating this procedure will be considered.