Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework of the Inverse Scattering Problem method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundary contours for them. We develop a method for obtaining explicit solutions to integrable boundary problems and its effectiveness is illustrated by series of examples.
The Hamiltonian structures of the two-dimensional Toda lattice and R-matrices
On the characterization of integrable systems via the Haantjes geometry
Comodule algebras and integrable systems
![QR code for arXiv:1012.3521 [math-ph]](http://oss.arxitics.com/images/favicon.svg)