Grassmannian flows and applications to non-commutative non-local and local integrable systems

We present a method for linearising classes of matrix-valued nonlinear partial differential equations with local and nonlocal nonlinearities. Indeed we generalise linearisation procedure originally developed by P\"oppe based on solving the corresponding underlying linear equation to generate an evolutionary Hankel operator `scattering data', then Fredholm akin Marchenko solution system. Our generalisation involves inflating system scattering data incorporate adjoint, reverse time or space-time data, it also allows operators kernels. With this approach show how linearise matrix Schr\"odinger modified Korteweg de Vries as well and/or versions these systems. Further, formulate unified that incorporates all systems special cases. Further still, demonstrate such are example Grassmannian flows.