Integrability in (2+1) dimensions: recent methods and results

Actual problems of the study of the nonlinear integrable equations are presented and proper modifications of the Inverse scattering transform are described by example of the famouse Kadomtsev–Petviashvili equation (more exactly, its version known as KPII). Review of the new results of the theory is given. This includes, in particular, a version of scattering problem over nontrivial background potential being a soliton solution of the KPII equation. Presentation is based essentially on the recent works with M. Boiti and F. Pempinelli.