Noncommutative geometry is based on an idea that an associative algebra can be regarded
as “an algebra of functions on a noncommutative space”. The major contribution to …

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 …

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 …

The nonlinear Schrödinger (NLS) equation, which incorporates higher-order dispersive
terms, is widely employed in the theoretical analysis of various physical phenomena. In this …

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 …

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 …

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 …

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 …

Interactions of noncommutative solitons in a modified U (n) sigma model in 2+ 1 dimensions
can be analyzed exactly. Using an extension of the dressing method, we construct explicit …