50 citations · 202 across the 30 of their papers we have counts for
9 papers · 1 filter
Linear systems, determinants and solutions of the Kadomtsev-Petviashvili equation
Gordon Blower, Simon J. Malham
Let be a linear system in continuous time with input and output space and state space . The scattering (or impulse response) functions $ϕ_{(x)}(t)…
Coagulation, non-associative algebras and binary trees
Simon J. A. Malham
We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associa…
Applications of Grassmannian flows to coagulation systems
Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis +1
We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as multiplicative Grassmannian flows and are therefore linearisable, and thus integrable in…
Integrability of local and nonlocal non-commutative fourth order quintic nonlinear Schrodinger equations
Simon J. A. Malham
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…
Grassmannian flows and applications to non-commutative non-local and local integrable systems
Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis
We present a method for linearising classes of matrix-valued nonlinear partial differential equations with local and nonlocal nonlinearities. Indeed we generalise a linearisation p…
Applications of Grassmannian flows to integrable systems
Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis +1
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fredholm Grassmannian flow…
Partial differential systems with nonlocal nonlinearities: Generation and solutions
Margaret Beck, Anastasia Doikou, Simon J. A. Malham +1
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions a…
Grassmannian flows and applications to nonlinear partial differential equations
Margaret Beck, Anastasia Doikou, Simon J. A. Malham +1
We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, fro…
Evans function and Fredholm determinants
Issa Karambal, Simon J. A Malham
We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line.…