The paper aims to demonstrate that a linear expansion in a unital two-dimensional algebra
can generate integrable couplings, proposing a novel approach for their construction. The …

This review is based on two lectures given at the 2000 TMR school in Torino (TMR school
on contemporary String Theory and Brane Physics, 26 January-2 February 2000, Torino …

We first reveal that there is a Riccati-type Miura transformation from the Fokas–Lenells (FL)
system to the first member of the negative part of the AKNS hierarchy. We derive a vectorial …

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 …

General soliton solutions to a reverse‐time nonlocal nonlinear Schrödinger (NLS) equation
are discussed via a matrix version of binary Darboux transformation. With this technique …

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 …

This study aims to explore the connection between integrable couplings and three-
dimensional unital algebras. Expansions in these algebras generate integrable couplings …

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 reveal the origin and structure of self-consistent source extensions of integrable
equations from the perspective of binary Darboux transformations. They arise via a …

In a number of recent publications, 1–4 Rauch-Wojciechowski, Marciniak, and Lundmark
have discussed an interesting class of systems of second-order ordinary differential …