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 …

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 …

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

Using the bicomplex approach we discuss an integrable noncommutative system in two-
dimensional Euclidean space. It is described by an equation of motion which reduces to the …

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

We study-function representation of solutions and deformation of Hirota bilinear relations for
a noncommutative Kadomtsev–Petviashvili (NC KP) hierarchy. An operator-valued-function …

We construct a deformation quantized version (ncKdV) of the KdV equation which
possesses an infinite set of conserved densities. Solutions of the ncKdV are obtained from …

Abstract Recently Scholtz and Geyer proposed a very efficient method to compute metric
operators for non-Hermitian Hamiltonians from Moyal products. We develop these ideas …