We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the...

We present a method for linearising classes of matrix-valued nonlinear partial differential equations with local and nonlocal nonlinearities. Indeed we generalise a linearisation procedure originally developed by Poppe based on solving the corresponding underlying linear partial differential...

We give a constructive proof, to all orders, that each member of the non-commutative potential Korteweg-de Vries hierarchy is a Fredholm Grassmannian flow and is therefore linearisable. Indeed we prove this for any linear combination of fields from this hierarchy. That each member of the...

We prove integrability of a generalised non-commutative fourth order quintic nonlinear Schrodinger equation. The proof is relatively succinct and rooted in the linearisation method pioneered by Ch. Poppe. It is based on solving the corresponding linearised partial differential system to generate...