Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Malham, Simon J. A."'
Autor:
Blower, Gordon, Malham, Simon J. A.
We prove that the non-commutative Kadomtsev-Petviashvili (KP) equation and a `lifted' modified Kadomtsev-Petviashvili (mKP) equation are directly linearisable, and thus integrable in this sense. There are several versions of the non-commutative mKP e
Externí odkaz:
http://arxiv.org/abs/2412.01686
Autor:
Malham, Simon J. A.
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-associative algebra generated by the convolution product of the coalescence t
Externí odkaz:
http://arxiv.org/abs/2307.00029
Autor:
Blower, Gordon, Malham, Simon J. A.
We prove that each member of the non-commutative nonlinear Schrodinger and modified Korteweg--de Vries hierarchy is a Fredholm Grassmannian flow, and for the given linear dispersion relation and corresponding equivalencing group of Fredholm transform
Externí odkaz:
http://arxiv.org/abs/2303.07324
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 this sense. First, we prove that a general Smoluchowski-type equation
Externí odkaz:
http://arxiv.org/abs/2201.05487
Autor:
Malham, Simon J. A.
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 t
Externí odkaz:
http://arxiv.org/abs/2108.04514
Autor:
Malham, Simon J. A.
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 line
Externí odkaz:
http://arxiv.org/abs/2009.14253
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this integral in te
Externí odkaz:
http://arxiv.org/abs/2008.08576
Publikováno v:
Physica D: Nonlinear Phenomena 415C (2021) 132744
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 P\"oppe based on solving the correspo
Externí odkaz:
http://arxiv.org/abs/2004.01789
Publikováno v:
CRM Series in Mathematical Physics, "Quantum Theory and Symmetries", pp 523-532, (2021)
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential equations, w
Externí odkaz:
http://arxiv.org/abs/2001.01637
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 flows. In other words, time-evolutionary solutions to such systems can be
Externí odkaz:
http://arxiv.org/abs/1905.05035