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Prof Allan P Fordy

Professor of Nonlinear Dynamics
Applied Mathematics

Contact details

Room: 8.23
Tel: +44 (0)113 3435115
Email: A.P.Fordy @ leeds.ac.uk

Keywords

Integrable Systems
Completely Integrable Hamiltonian Systems
Mathematical Physics
Cluster Algebras
Integrable Maps
Superintegrability and Poisson Algebras

Research interests

My main research interests lie within Integrable Systems. Most of my research has been of an algebraic nature: the classification of Lax pairs through Lie algebras and symmetric spaces; Hamiltonian structures and Miura maps; stationary flows and the reduction of Poisson brackets; symmetries and superintegrability in quantum integrable systems; Poisson algebras related to classical superintegrable systems; integrable maps related to cluster algebras and associated Poisson algebras.

The main thrust of my recent research has been in various aspects of integrable maps.

In particular we recently introduced a new class of mutation-periodic quivers and gave a full classification of the period one case. Later papers are analysing and classifying the associated integrable maps.

Useful links

Integrable Systems Group
Personal Home Page
Google Scholar Research Profile

Publications

Fordy AP, Xenitidis P Self-dual systems, their symmetries and reductions to the Bogoyavlensky lattice Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 13, 2017
DOI:10.3842/SIGMA.2017.051
View abstract

Fordy AP, Xenitidis P ZN graded discrete Lax pairs and Yang–Baxter maps Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 473, 20160946-20160946, 2017
DOI:10.1098/rspa.2016.0946

Fordy AP A note on some superintegrable Hamiltonian systems Journal of Geometry and Physics, 115, 98-103, 2017
DOI:10.1016/j.geomphys.2016.06.005

Fordy AP, Xenitidis P ${{\mathbb{Z}}_{N}}$ graded discrete Lax pairs and integrable difference equations Journal of Physics A: Mathematical and Theoretical, 50, 165205-165205, 2017
DOI:10.1088/1751-8121/aa639a

Fordy AP Periodic cluster mutations and related integrable maps JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 47, 2014
DOI:10.1088/1751-8113/47/47/474003

Fordy AP, Hone A Discrete Integrable Systems and Poisson Algebras From Cluster Maps COMMUNICATIONS IN MATHEMATICAL PHYSICS, 325, 527-584, 2014
DOI:10.1007/s00220-013-1867-y

Fordy AP, Kassotakis P Integrable maps which preserve functions with symmetries Journal of Physics A: Mathematical and Theoretical, 46, 2013
DOI:10.1088/1751-8113/46/20/205201
View abstract

Fordy AP, Scott MJ Recursive procedures for Krall-Sheffer operators Journal of Mathematical Physics, 54, 2013
DOI:10.1063/1.4802098
View abstract

Fordy AP, Marsh RJ Cluster mutation-periodic quivers and associated Laurent sequences J ALGEBR COMB, 34, 19-66, 2011
DOI:10.1007/s10801-010-0262-4

Fordy AP Mutation-periodic quivers, integrable maps and associated Poisson algebras PHILOS T R SOC A, 369, 1264-1279, 2011
DOI:10.1098/rsta.2010.0318

Fordy AP, Hone A Symplectic Maps from Cluster Algebras Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7, 2011
DOI:10.3842/SIGMA.2011.091
View abstract

Fordy AP Quantum Super-Integrable Systems as Exactly Solvable Models SYMMETRY INTEGR GEOM, 3, 2007

Fordy AP Darboux related quantum integrable systems on a constant curvature surface Journal of Geometry and Physics, 56, 1709-1727, 2006
DOI:10.1016/j.geomphys.2005.10.001
View abstract

Fordy AP, Kassotakis PG Multidimensional maps of QRT type J PHYS A-MATH GEN, 39, 10773-10786, 2006
DOI:10.1088/0305-4470/39/34/012

Fordy AP Symmetries, Ladder Operators and Quantum Integrable systems Glasgow Mathematical Journal, 47A, 65-75, 2005
DOI:10.1017/S0017089505002296
View abstract

Fordy AP, Mokhov OI On a special class of compatible Poisson structures of hydrodynamic type Physica D - Nonlinear Phenomena, 152-153, 475-490, 2001
DOI:10.1016/S0167-2789(01)00187-7
View abstract

Fordy AP, Gurel TB A New Construction of Recursion Operators for Systems of Hydrodynamic Type Theoretical and Mathematical Physics, 122, 29-38, 2000
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Fordy AP Systems of hydrodynamic type from Poisson commuting HamiltoniansMeeting on Integrability - The Seiberg-Witten and Whitham Equations, 229-249 2000
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Ferapontov EV, Fordy AP Commuting Quadratic Hamiltonians with Velocity Dependent Potentials Reports on Mathematical Physics, 44, 71-80, 1999
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Ferapontov EV, Fordy AP Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term Physica D: Nonlinear Phenomena, 108, 350-364, 1997
DOI:10.1016/S0167-2789(97)00040-7

Fordy AP, Harris SD Hamiltonian Flows on Stationary Manifolds Methods and Applications of Analysis, 4, 212-238, 1997
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Ferapontov EV, Fordy AP Separable Hamiltonians and Integrable Systems of Hydrodynamic Type Journal of Geometry and Physics, 21, 169-182, 1997
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Fordy AP, Shabat AB, Veselov AP Factorization and Poisson correspondences Theoretical and Mathematical Physics, 105, 1369-1386, 1995
DOI:10.1007/BF02070933

Fordy AP Stationary flows: Hamiltonian structures and canonical transformations Physica D: Nonlinear Phenomena, 87, 20-31, 1995
DOI:10.1016/0167-2789(95)00134-P

Baker S, Enolskii VZ, Fordy AP Integrable quartic potentials and coupled KdV equations Physics Letters A, 201, 167-174, 1995
DOI:10.1016/0375-9601(95)00267-7

Conte R, Fordy AP, Pickering A A perturbative Painlevé approach to nonlinear differential equations Physica D: Nonlinear Phenomena, 69, 33-58, 1993
DOI:10.1016/0167-2789(93)90179-5

Fordy AP, Holm DD A tri-Hamiltonian formulation of the self-induced transparency equations Physics Letters A, 160, 143-148, 1991
DOI:10.1016/0375-9601(91)90603-6

Fordy A, Pickering A Analysing negative resonances in the Painlevé test Physics Letters A, 160, 347-354, 1991
DOI:10.1016/0375-9601(91)90663-S

Fordy AP The Hénon-Heiles system revisited Physica D: Nonlinear Phenomena, 52, 204-210, 1991
DOI:10.1016/0167-2789(91)90122-P

Antonowicz M, Fordy AP, Liu QP Energy-dependent third-order Lax operators Nonlinearity, 4, 669-684, 1991
DOI:10.1088/0951-7715/4/3/003

Antonowicz M, Fordy AP Factorisation of energy dependent Schr�dinger operators: Miura maps and modified systems Communications in Mathematical Physics, 124, 465-486, 1989
DOI:10.1007/BF01219659

Antonowicz M, Fordy AP Super-extensions of energy dependent Schr�dinger operators Communications in Mathematical Physics, 124, 487-500, 1989
DOI:10.1007/BF01219660

Fordy AP, Reyman AG, Semenov-Tian-Shansky MA Classical r-matrices and compatible Poisson brackets for coupled KdV systems Letters in Mathematical Physics, 17, 25-29, 1989
DOI:10.1007/BF00420010

Antonowicz M, Fordy AP Coupled Harry Dym equations with multi-Hamiltonian structures Journal of Physics A: Mathematical and General, 21, L269-L275, 1988
DOI:10.1088/0305-4470/21/5/001

Antonowicz M, Fordy AP Coupled KdV equations with multi-Hamiltonian structures Physica D: Nonlinear Phenomena, 28, 345-357, 1987
DOI:10.1016/0167-2789(87)90023-6

Fordy A, Athorne C Generalized Davey-Stewartson equations associated with symmetric spaces Physica D: Nonlinear Phenomena, 28, 248-248, 1987
DOI:10.1016/0167-2789(87)90206-5

Fordy A Some completely integrable classical mechanical systems associated with symmetric spaces Physica D: Nonlinear Phenomena, 28, 242-242, 1987
DOI:10.1016/0167-2789(87)90191-6

Antonowicz M, Fordy AP, Wojciechowski S Integrable stationary flows: Miura maps and bi-hamiltonian structures Physics Letters A, 124, 143-150, 1987
DOI:10.1016/0375-9601(87)90241-6

Athorne C, Fordy A Integrable equations in (2+1) dimensions associated with symmetric and homogeneous spaces Journal of Mathematical Physics, 28, 2018-2024, 1987
DOI:10.1063/1.527463

Antonowicz M, Fordy AP A family of completely integrable multi-hamiltonian systems Physics Letters A, 122, 95-99, 1987
DOI:10.1016/0375-9601(87)90783-3

Athorne C, Fordy A Generalised KdV and MKdV equations associated with symmetric spaces Journal of Physics A: Mathematical and General, 20, 1377-1386, 1987
DOI:10.1088/0305-4470/20/6/021

Fordy A, Wojciechoski S, Marshall I A family of integrable quartic potentials related to symmetric spaces Physics Letters A, 113, 395-400, 1986
DOI:10.1016/0375-9601(86)90658-4

Dodd RK, Fordy AP Prolongation structures of complex quasi-polynomial evolution equations Journal of Physics A: Mathematical and General, 17, 3249-3266, 1984
DOI:10.1088/0305-4470/17/16/025

Fordy AP Derivative nonlinear Schrodinger equations and Hermitian symmetric spaces Journal of Physics A: Mathematical and General, 17, 1235-1245, 1984
DOI:10.1088/0305-4470/17/6/019

Fordy AP, Kulish PP Nonlinear Schr�dinger equations and simple Lie algebras Communications in Mathematical Physics, 89, 427-443, 1983
DOI:10.1007/BF01214664

Fordy AP Hamiltonian symmetries of the Henon-Heiles system Physics Letters A, 97, 21-23, 1983
DOI:10.1016/0375-9601(83)90091-9

Dodd R, Fordy A The Prolongation Structures of Quasi-Polynomial Flows Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 385, 389-429, 1983
DOI:10.1098/rspa.1983.0020

Bullough RK, Fordy AP, Manakov SV Adiabatic invariants theory of near-integrable systems with damping Physics Letters A, 91, 98-100, 1982
DOI:10.1016/0375-9601(82)90358-9

Dodd R, Fordy A On the integrability of a system of coupled KdV equations Physics Letters A, 89, 168-170, 1982
DOI:10.1016/0375-9601(82)90199-2

Fordy AP, Gibbons J Factorization of operators.II Journal of Mathematical Physics, 22, 1170-1175, 1981
DOI:10.1063/1.525041

Fordy AP, Gibbons J Integrable nonlinear Klein-Gordon equations and Toda lattices Communications in Mathematical Physics, 77, 21-30, 1980
DOI:10.1007/BF01205037

Fordy AP, Gibbons J Some remarkable nonlinear transformations Physics Letters A, 75, 325-325, 1980
DOI:10.1016/0375-9601(80)90829-4

Fordy AP, Gibbons J Factorization of operators I. Miura transformations Journal of Mathematical Physics, 21, 2508-2508, 1980
DOI:10.1063/1.524357

Fordy AP Higher-spin fields in a curved space-time General Relativity and Gravitation, 9, 387-392, 1978
DOI:10.1007/BF00759839

Fordy AP Zero-rest-mass fields in an algebraically special curved space-time General Relativity and Gravitation, 8, 227-243, 1977
DOI:10.1007/BF00765810

Fordy AP; Huang Q Poisson Algebras and 3D Superintegrable Hamiltonian Systems.
View abstract

Fordy AP; Xenitidis P ${\mathbb{Z}}_N$ graded discrete Lax pairs and discrete integrable systems.
View abstract

Fordy AP; Xenitidis P ${\mathbb{Z}}_N$ graded discrete Lax pairs and Yang-Baxter maps.
View abstract