This thesis is designed for a comprehensive review of noncommutative (BPS) solitons with
applications to D-brane dynamics including our works. We focus on noncommutative …

We present a powerful method to generate various equations which possess the Lax
representations on noncommutative (1+ 1)-and (1+ 2)-dimensional spaces. The generated …

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These
solutions are expressed in terms of quasideterminants, constructed by means of Darboux …

We present a noncommutative version of the Burgers equation which possesses the Lax
representation and discuss the integrability in detail. We find a noncommutative version of …

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of
equations are presented. The class corresponds to a Lax operator with entries in a …

We study the noncommutative generalization of (Euclidean) integrable models in two
dimensions, specifically the sine-and sinh-Gordon and the U (N) principal chiral models. By …

We discuss commuting flows and conservation laws for Lax hierarchies on noncommutative
spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has …

Requiring an infinite number of conserved local charges or the existence of an underlying
linear system does not uniquely determine the Moyal deformation of (1+ 1)-dimensional …

Non-commutative Ward's conjecture is a non-commutative version of the original Ward's
conjecture which says that almost all integrable equations can be obtained from anti-self …

Bidifferential graded algebras and integrable systems Page 1 arXiv:0805.4553v3 [nlin.SI] 30
Jun 2008 Bidifferential graded algebras and integrable systems ARISTOPHANES DIMAKIS …