4 papers
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 $Ï_{(x)}(t…
The noncommutative KP hierarchy and its solution via descent algebra
Gordon Blower, Simon J. A. Malham
We give the solution to the complete noncommutative Kadomtsev--Petviashvili (KP) hierarchy. We achieve this via direct linearisation which involves the Gelfand--Levitan--Marchenko…
Direct Inversion for the Squared Bessel Process and Applications
Simon J. A. Malham, Anke Wiese, Yifan Xu
In this paper we derive a new direct inversion method to simulate squared Bessel processes. Since the transition probability of these processes can be represented by a non-central…
Direct linearisation of the non-commutative Kadomtsev-Petviashvili equations
Gordon Blower, Simon J. A. Malham
We prove that the non-commutative Kadomtsev-Petviashvili (KP) equation and a `lifted' modified Kadomtsev-Petviashvili (mKP) equation are directly linearisable, and thus integrable…