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 …

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 …

We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the
Yang-Mills equations on the noncommutative space R θ 2 n× S 2 which have manifest …

We extend the analysis of hep-th/0408069 on a Lorentz invariant interpretation of
noncommutative spacetime to field theories on non-anticommutative superspace with half …

We consider equivariant dimensional reduction of Yang-Mills theory on Kähler manifolds of
the form M× Bbb CP 1× Bbb CP 1. This induces a rank two quiver gauge theory on M which …

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills
equation where the gauge group is G= GL (2), and use it to generate a series of exact …

We discuss an extension of soliton theory and integrable systems to noncommutative
spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang–Mills …