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Prof Alexander V Mikhailov

Professor of Mathematical Physics
Applied Mathematics

Contact details

Room: 9.305
Tel: +44 (0)113 3435176
Email: A.V.Mikhailov @ leeds.ac.uk

Keywords

Classification of integrable systems
Integrability of differential and difference equations
Algebraic theory of differential and difference equations
Classification of Lax oprators and reduction problem
Automorphic and quasi-graded Lie algebras
Invers spectral transform
Soliton theory
Multi-scaling asymptotics

Useful links

Integrable Systems Group
My homepage
Publications

Current postgraduate students

George Berkeley (2012)

Publications

Mikhailov AV, Papamikos G, Wang JP Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere Letters in Mathematical Physics, 106, 973-996, 2016
DOI:10.1007/s11005-016-0855-5
View abstract

Mikhailov AV, Papamikos G, Wang JP Dressing method for the vector sine-Gordon equation and its soliton interactions Physica D: Nonlinear Phenomena, 325, 53-62, 2016
DOI:10.1016/j.physd.2016.01.010
View abstract

Grahovski GG, Konstantinou-Rizos S, Mikhailov AV Grassmann extensions of Yang-Baxter maps Journal of Physics A: Mathematical and Theoretical, 49, 2016
DOI:10.1088/1751-8113/49/14/145202
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Mikhailov AV, Papamikos G, Wang JP Darboux transformation with dihedral reduction group JOURNAL OF MATHEMATICAL PHYSICS, 55, 2014
DOI:10.1063/1.4901224

Garifullin RN, Mikhailov AV, Yamilov RI Discrete equation on a square lattice with a nonstandard structure of generalized symmetries Theoretical and Mathematical Physics, 180, 765-780, 2014
DOI:10.1007/s11232-014-0178-6
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Konstantinou-Rizos S, Mikhailov AV Yang-Baxter maps and finite reduction groups with degenerated orbits Journal of Physics A: Mathematical and Theoretical, 2014

Grahovski GG, Mikhailov AV Integrable discretisations for a class of nonlinear Schrodinger equations on Grassmann algebras Physics Letters A, 377, 3254-3259, 2013
DOI:10.1016/j.physleta.2013.10.018
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Khanizadeh F, Mikhailov AV, Wang JP Darboux transformations and Recursion operators for differential--difference equations Theoretical and Mathematical Physics, 177, 1606-1654, 2013
DOI:10.1007/s11232-013-0124-z
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Mikhailov AV; Xenitidis P Second order integrability conditions for difference equations: an integrable equation. 2013
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Konstantinou-Rizos S, Mikhailov A Darboux transformations, finite reduction groups and related Yang-Baxter maps Journal of Physics A: Mathematical and Theoretical, 46, 2012
DOI:10.1088/1751-8113/46/42/425201
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Gerdjikov V, Grahovski G, Valchev T, Mikhailov A On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Su(3)/S(U(1)× U(2)) Symmetric Space Journal of Geometry and Symmetry in Physics, 25, 23-55, 2012
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Mikhailov AV, Wang JP A new recursion operator for Adler’s equation in the Viallet form Physics Letters, Section A: General, Atomic and Solid State Physics, 375, 3960-3963, 2011
DOI:10.1016/j.physleta.2011.09.018
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Mikhailov AV, Wang JP, Xenitidis P Cosymmetries and Nijenhuis recursion operators for difference equations Nonlinearity, 24, 2079-2097, 2011
DOI:10.1088/0951-7715/24/7/009
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Gerdjikov VS, Grahovski GG, Mikhailov AV, Valchev TI RATIONAL BUNDLES AND RECURSION OPERATORS FOR INTEGRABLE EQUATIONS ON A.III-TYPE SYMMETRIC SPACES THEOR MATH PHYS+, 167, 740-750, 2011

Mikhailov AV, Wang JP, Xenitidis P RECURSION OPERATORS, CONSERVATION LAWS, AND INTEGRABILITY CONDITIONS FOR DIFFERENCE EQUATIONS THEOR MATH PHYS+, 167, 421-443, 2011

Gerdjikov VS, Grahovski GG, Mikhailov AV, Valchev TI Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces SYMMETRY INTEGR GEOM, 7, 2011
DOI:10.3842/SIGMA.2011.096

Gerdjikov VS, Mikhailov AV, Valchev TI Recursion operators and reductions of integrable equations on symmetric spaces Journal of Geometry and Symmetry in Physics, 20, 1-34, 2010
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Gerdjikov VS, Mikhailov AV, Valchev TI Reductions of integrable equations on A.III-type symmetric spaces Journal of Physics A: Mathematical and Theoretical, 43, 2010
DOI:10.1088/1751-8113/43/43/434015
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Bhatt R; Mikhailov AV (2010) On the inconsistency of the Camassa-Holm model with the shallow water theory.
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Gurevich AV, Kuznetsov EA, Mesyats GA, Mikhailov AV, Musher SL, Novikov SP, Rubenchik AM, Sagdeev RZ, Smirnov GI, Sinai YG, Skrinsky AN, Fortov VE Vladimir Evgen'evich Zakharov (on his 70th birthday) PHYS-USP+, 52, 863-864, 2009
DOI:10.3367/UFNe.0179.200908n.0917

Mikhailov AV Integrability. Berlin, Heidelberg: Springer 2009
DOI:10.1007/978-3-540-88111-7
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Mikhailov A, Sokolov V Symmetries of Differential Equations and the problem of Integrability In Integrability, 19-88, 2009
DOI:10.1007/978-3-540-88111-7

Mikhailov AV, Novikov VS, Wang JP Symbolic representation and classification of integrable systems In Algebraic Theory of Differential Equations, 156-216, 2009

MacCallum MAH; Mikhailov AV Algebraic Theory of Differential Equations. Cambridge: Cambridge University Press 2009

Mikhailov A Introduction In Integrability, 1-18, 2009
DOI:10.1007/978-3-540-88111-7

Mikhailov AV, Novikov VS, Wang JP On classification of integrable nonevolutionary equations Studies in Applied Mathematics, 118, 419-457, 2007
DOI:10.1111/j.1467-9590.2007.00376.x
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Lombardo S, Mikhailov AV Reduction groups and automorphic Lie algebras Communications in Mathematical Physics, 258, 179-202, 2005
DOI:10.1007/s00220-005-1334-5
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Mikhailov AV, Novikov VS, Wang JP Partially integrable nonlinear equations with one higher symmetry Journal of Physics A: Mathematical and General, 38, L337-L341, 2005
DOI:10.1088/0305-4470/38/20/L02
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Lombardo S; Mikhailov AV Reductions of integrable equations and automorphic Lie algebrasConference on Symmetry and Perturbation Theory, 183-192 2005
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Lombardo S, Mikhailov AV Reductions of integrable equations: dihedral group Journal of Physics A: Mathematical and General, 37, 7727-7742, 2004
DOI:10.1088/0305-4470/37/31/006
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Mikhailov AV; Novokshenov VY The Riemann-Hilbert problem for analytic description of the DM solitonsTHEOR MATH PHYS+, 1723-1732 2003
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Mikhailov AV, Novikov VS Classification of Integrable Benjamin—Ono-Type Equations Moscow Mathematical Journal, 3, 1293-1305, 2003

Mikhailov AV, Novokshenov VY Period map for nonlinear pulses in optical dispersion-managed fibers THEOR MATH PHYS+, 134, 107-116, 2003
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Mikhailov AV, Santini PM Nonlinear Evolution Equations and Dynamical Systems Theoretical and Mathematical Physics, 134, 1-40, 2003
DOI:10.1023/A:1021875924760

Mikhailov AV, Novikov VS Perturbative symmetry approach Journal of Physics A: Mathematical and General, 35, 4775-4790, 2002
DOI:10.1088/0305-4470/35/22/309
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Mikhailov AV, Santini PM Nonlinear Evolution Equations and Dynamical Systems Theoretical and Mathematical Physics, 133, 1607-1756, 2002
DOI:10.1023/A:1021396022516

Kodama Y, Mikhailov AV Symmetry and perturbation of the vector nonlinear Schrodinger equation PHYSICA D, 152, 171-177, 2001

Turitsyn SK, Mikhailov AV Application of soloitons In Scattering, 1741-1753, 2001

Mikhailov AV, Novokshenov VY The period map for pulse propagation in nonlinear optical DM fibers JETP LETT+, 73, 250-254, 2001

Mikhailov AV, Sokolov VV Integrable ODEs on Associative Algebras Communications in Mathematical Physics, 211, 231-251, 2000
DOI:10.1007/s002200050810
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Leon J, Mikhailov AV Raman Soliton Generation From Laser Inputs in SRS Physics Letters. Section A: General, Atomic and Solid State Physics, 253, 33-40, 1999
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Galeev AA; Kuznetsov EA; Mikhailov AV; Nesterikhin YE; Novikov SP; Sagdeev RZ; Sinai YG; Smirnov GI; Fortov VE; Khalatnikov IM Vladimir Evgenevich Zakharov (on his sixtieth birthday). 169, 1161-1162 1999

Zakharov VE ed. Transient Raman amplification 1999

Zakharov VEWS ed. Variationalism and empirio-criticism. (Exact and Variational Approaches to fibre optics equations) 1999

Mikhailov AV, Yamilov RI Towards classification of (2 + 1)-dimensional integrable equations. Integrability conditions I Journal of Physics A: Mathematical and General, 31, 6707-6715, 1998
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Leon J; Mikhailov AV Raman Solitons and Raman spikes. 1997
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Kodama Y, Mikhailov AV, Wabnitz S Input Pulse Optimization in Wavelength-Division-Multiplexed Soliton Transmissions Optics Communications, 143, 53-56, 1997
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Montes C, Mikhailov A, Picozzi A, Ginovart F Dissipative three-wave structures in stimulated backscattering .1. A subluminous solitary attractor PHYSICAL REVIEW E, 55, 1086-1091, 1997
DOI:10.1103/PhysRevE.55.1086

Mikhailov AV; Yamilov RI On integrable two-dimensional generalizations of nonlinear Schrodinger type equations. 230, 295-300 1997

Mikhailov AV; Kuznetsov EA; Newell AC; Zakharov VE THE NONLINEAR SCHRODINGER-EQUATION - PROCEEDINGS OF THE CONFERENCE ON THE NONLINEAR SCHRODINGER-EQUATION - CHERNOGOLOVKA, 25 JULY 3 AUGUST 1994. 87, R7-R9 1995

Kuznetsov EA; Mikhailov AV; Shimokhin IA NONLINEAR-INTERACTION OF SOLITONS AND RADIATION. 87, 201-215 1995

Kuznetsov EA; Mikhailov AV RELAXATION OSCILLATIONS OF SOLITONS. 60, 486-490 1994

Devega HJ; Mikhailov AV; Sanchez N EXACT STRING SOLUTIONS IN (2+1)-DIMENSIONAL DESITTER SPACE-TIME. 9, 2745-2754 1994

Devega HJ, Mikhailov AV, Sanchez N NEW SOLUTIONS OF THE CLASSICAL STRING EQUATION IN DESITTER SPACE In Nonlinear Coherent Structures in Physics and Biology, 271-274, 1994

Combes F, Vega HJD, Mikhailov AV, Sánchez N Multi-String Solutions by Soliton Methods in De Sitter Spacetime Physical Review D, 50, 2754-2768, 1993
DOI:10.1103/PhysRevD.50.2754
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Vega HJD, Mikhailov AV, Sanchez N Exact String Solutions in 2+1-Dimensional De Sitter Spacetime Theoretical and Mathematical Physics, 94, 166-172, 1993
DOI:10.1007/BF01019328
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Mikhailov AV; Shimokhin IA SPECTRUM OF 180-DEGREES BLOCH-TYPE DOMAIN-WALL EXCITATIONS IN YTTRIUM-IRON-GARNET. 48, 9569-9574 1993

Mikhailov AV; Wabnitz S POLARIZATION DYNAMICS OF COUNTERPROPAGATING BEAMS IN OPTICAL FIBERS. 15, 1055-1057 1990

Conte RBN ed. A CONCEPT OF INTEGRABILITY BASED ON THE SYMMETRY APPROACH. 310th ed 1990

Mikhailov AV; Shimokhin IA DOMAIN-WALL EXCITATION SPECTRUM IN UNIAXIAL FERROMAGNET. 97, 1966-1973 1990

Mikhailov AV; Shabat AB; Yamilov RI EXTENSION OF THE MODULE OF INVERTIBLE TRANSFORMATIONS - CLASSIFICATION OF INTEGRABLE SYSTEMS. 115, 1-19 1988

Mikhailov AV; Shabat AB; Iamilov RI ON THE EXTENSION OF REVERSIBLE TRANSFORMATION MODULE. 295, 288-291 1987

Mikhailov AV; Shabat AB; Yamilov RI THE SYMMETRY APPROACH TO THE CLASSIFICATION OF NON-LINEAR EQUATIONS - COMPLETE LISTS OF INTEGRABLE SYSTEMS. 42, 1-63 1987

Burtsev SP; Zakharov VE; Mikhailov AV INVERSE SCATTERING METHOD WITH VARIABLE SPECTRAL PARAMETER. 70, 227-240 1987

Zakharov VE; Mikhailov AV POLARIZATION DOMAINS IN NONLINEAR OPTICS. 45, 349-352 1987

Mikhailov AV; Shabat AB INTEGRABILITY CONDITIONS FOR SYSTEMS OF 2 EQUATIONS OF THE FORM UT = A(U)UXX + F(U, UX) .2. 66, 31-44 1986

Mikhailov AV; Shabat AB INTEGRABLE DEFORMATIONS OF THE HEISENBERG-MODEL. 116, 191-194 1986

Mikhailov AV; Shabat AB INTEGRABILITY CONDITIONS FOR SYSTEMS OF 2 EQUATIONS OF THE FORM UT = A(U)UXX + F(U,UX) .1. 62, 107-122 1985

Gabitov IR; Zakharov VE; Mikhailov AV MAXWELL-BLOCH EQUATION AND THE INVERSE SCATTERING METHOD. 63, 328-343 1985

Gabitov IR; Zakharov VE; Mikhailov AV NONLINEAR-THEORY OF SUPERFLUORESCENCE. 86, 1204-1216 1984

Mikhailov AV; Yaremchuk AI FORCED MOTION OF A DOMAIN-WALL IN THE FIELD OF SPIN-WAVE. 39, 354-357 1984

Zakharov VE; Mikhailov AV METHOD OF THE INVERSE SCATTERING PROBLEM WITH SPECTRAL PARAMETER ON AN ALGEBRAIC CURVE. 17, 247-251 1983

Gabitov IR; Zakharov VE; Mikhailov AV SUPERFLUORESCENCE PULSE SHAPE. 37, 279-282 1983

Mikhailov AV RELATIVISTICALLY INVARIANT MODELS OF THE FIELD-THEORY INTEGRABLE BY THE INVERSE SCATTERING METHOD. 970, 186-196 1982

Mikhailov AV THE LANDAU-LIFSCHITZ EQUATION AND THE RIEMANN BOUNDARY-PROBLEM ON A TORUS. 92, 51-55 1982

Mikhailov AV; Yaremchuk AI AXIALLY SYMMETRICAL SOLUTIONS OF THE TWO-DIMENSIONAL HEISENBERG-MODEL. 36, 95-100 1982

Mikhailov AV; Yaremchuk AI CYLINDRICALLY SYMMETRIC-SOLUTIONS OF THE NON-LINEAR CHIRAL FIELD MODEL (SIGMA-MODEL). 202, 508-522 1982

Mikhailov AV THE REDUCTION PROBLEM AND THE INVERSE SCATTERING METHOD. 3, 73-117 1981

Mikhailov AV; Olshanetsky MA; Perelomov AM TWO-DIMENSIONAL GENERALIZED TODA LATTICE. 79, 473-488 1981

Lvov VS; Mikhailov AV CONTRIBUTION TO THE NON-LINEAR THEORY OF SOUND AND HYDRODYNAMIC TURBULENCE OF A COMPRESSIBLE LIQUID. 2, 224-243 1981

Kuznetsov EA; Mikhailov AV ON THE TOPOLOGICAL MEANING OF CANONICAL CLEBSCH VARIABLES. 77, 37-38 1980

Mikhailov AV REDUCTION IN INTEGRABLE SYSTEMS - THE REDUCTION GROUP. 32, 174-178 1980

Zakharov VE; Mikhailov AV ON THE INTEGRABILITY OF CLASSICAL SPINOR MODELS IN TWO-DIMENSIONAL SPACE-TIME. 74, 21-40 1980

Mikhailov AV; Perelomov AM INSTANTON-TYPE SOLUTIONS IN SUPER-SYMMETRICAL CHIRAL MODELS. 29, 403-407 1979

Mikhailov AV INTEGRABILITY OF A TWO-DIMENSIONAL GENERALIZATION OF THE TODA CHAIN. 30, 414-418 1979

Mikhailov AV INTEGRABILITY OF SUPERSYMMETRICAL GENERALIZATIONS OF CLASSICAL CHIRAL MODELS IN 2-DIMENSIONAL SPACE-TIME. 28, 512-516 1978

Lvov VS; Mikhailov AV SCATTERING AND INTERACTION OF SOUND WITH SOUND IN A TURBULENT MEDIUM. 75, 1669-1682 1978

Lvov VS; Mikhailov AV SOUND AND HYDRODYNAMIC TURBULENCE IN A COMPRESSIBLE LIQUID. 74, 1445-1457 1978

Zakharov VE; Mikhailov AV EXAMPLE OF NONTRIVIAL INTERACTION OF SOLITONS IN 2-DIMENSIONAL CLASSICAL FIELD-THEORY. 27, 42-46 1978

Zakharov VE; Mikhailov AV RELATIVISTICALLY INVARIANT 2-DIMENSIONAL MODELS IN FIELD-THEORY INTEGRABLE BY INVERSE PROBLEM TECHNIQUE. 74, 1953-1973 1978

Kuznetsov EA; Mikhailov AV COMPLETE INTEGRABILITY OF 2-DIMENSIONAL CLASSICAL THIRRING MODEL. 30, 193-200 1977

Mikhailov AV INTEGRABILITY OF 2-DIMENSIONAL THIRRING MODEL. 23, 320-323 1976

Kuznetso.Ea; Mikhailo.Av STABILITY OF STATIONARY WAVES IN NONLINEAR WEAKLY DISPERSIVE MEDIA. 67, 1717-1727 1974

Mikhailov AV, Konstantinou-Rizos S Anticommutative extension of the Adler map Journal of Physics A: Mathematical and Theoretical
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