List of publications



Editing Separate Issues and Books

  1. A.V. Mikhailov, E.A. Kuznetsov, A.C. Newell and V.E. Zakharov ``The Nonlinear Schrödinger Equation'', guest editors of a special issue, Physica D 87, No 1-4, pp. 1-380, North Holland, 1995.

  2. A.P. Fordy and A.V. Mikhailov ``Nonlinear Evolution Equations and Dynamical Systems'', guest editors of a special issue, Theoretical and Mathematical Physics 122 No 1, pp. 1-134.

  3. A.P. Fordy and A.V. Mikhailov ``Nonlinear Evolution Equations and Dynamical Systems'', guest editors of a special issue, Theoretical and Mathematical Physics No 2, pp. 135-268, 2000.

  4. A.V. Mikhailov and P.M. Santini, ``Nonlinear Evolution Equations and Dynamical Systems'', guest editors of a special issue, Theoretical and Mathematical Physics 133 No 2, pp. 1443-1606, 2002.

  5. A.V. Mikhailov and P.M. Santini, ``Nonlinear Evolution Equations and Dynamical Systems'', guest editors of a special issue, Theoretical and Mathematical Physics 133 No 3, pp. 1607-1756, 2002.

  6. A.V. Mikhailov and P.M. Santini, ``Nonlinear Evolution Equations and Dynamical Systems'', guest editors of a special issue, Theoretical and Mathematical Physics 134 No 1, pp. 1-140, 2003.

  7. MacCallum MAH, Mikhailov AV,”Algebraic Theory of Differential Equations”,1-240, Cambridge University Press, Cambridge 2009 Publisher weblink

  8. Mikhailov AV,”Integrability”,1-359. Springer, Berlin, Heidelberg 2009

    Parts of Books

  9. A.V. Mikhailov, ``Relativistically Invariant Models of a Field Theory Integrable by the Inverse Scattering Method'', Lecture Notes in Mathematical v.970, p.186-196, Berlin, Heidelberg, New-York, London, Paris, Springer Verlag, 1982

  10. A.V. Mikhailov, ``Integrable Magnetic Models'', ed. by V.E. Zakharov, V.L. Pokrovskii and S.E. Trullinger, in book ``Solitons'', ``Modern Problem in Condensed matter'', v.17, p.623-690, Elsevier Science Publishers B.V., 1986

  11. I.R. Gabitov and A.V. Mikhailov, ``Superfluorescence Under Atomic Level Ddegeneration'', ``Plasma Theory, Nonlinear and Turbulent Processes in Physics'', Book of Selected Papers, vol. 2, pp. 779-787, World Scientific, 1988

  12. A.V. Mikhailov, A.B. Shabat and V.V. Sokolov, ``Classification of Integrable Equations'', ed. V.G. Bar'yakhtar, V.E. Zakharov, V.M. Chernousenko, in book ``Integrability and Kinetic Equations for Solitons'', pp. 213-279, Kiev, Naukova dumka, 1990

  13. A.V. Mikhailov, V.V. Sokolov and A.B. Shabat, ``The Symmetry Approach to Classification of Integrable Equations'', ed. by V.E. Zakharov, in book ``What is Integrability?'', pp. 113-184, Berlin, Heidelberg, New-York, London, Paris, Tokio, Hong Kong, Barcelona, Springer Verlag, 1991

  14. A.V. Mikhailov and A.B. Shabat, ``Symmetries - Tests of Integrability'', ed. by A. Fokas and V.E. Zakharov, in book ``Important Developments in Soliton Theory'', pp 355-374, Berlin, Heidelberg, New-York, London, Paris, Tokio, Hong Kong, Barcelona, Budapest, Springer Verlag, 1993

  15. A.V. Mikhailov and I.A. Shimokhin, ``Spectrum of Domain Wall Excitations in YIG'', ed. by A.S. Fokas, D.J. Kaup, A.C. Newell and V.E. Zakharov, in book ``Nonlinear Processes in Physics'', pp. 47-52, Berlin, Heidelberg, New-York, London, Paris, Tokio, Hong Kong, Barcelona, Budapest, Springer Verlag, 1993

  16. A.V. Mikhailov, H.J. de Vega and N. Sánchez, ``New Solutions of the classical String Equations in De Sitter Space'', ed. by K.H. Spatschek and F.G. Mertens, in the book ``Nonlinear Coherent Structures in Physics and Biology'', NATO ASI Series B: Physics Vol. 329, pp. 271-274, New York, Plenum Press, 1994

  17. Y. Kodama and A.V. Mikhailov, ``Obstacles to Asymptotic Integrability'', ed. I.M. Gelfand and A. Fokas, in book ``Algebraic aspects of Integrability'', pp 173-204, Boston, Basel, Berlin, Birkhauser, 1996

  18. A.V. Mikhailov, ``Variationalism and Empirio-criticism. (Exact and variational approaches to fibre optics equations.)'', ed. V.E. Zakharov and S. Wabnitz, in book ``Optical Solitons: Theoretical challenges and Industrial Perspectives'', pp 63-72, Berlin, Heidelberg; Springer, 1999

  19. J. Leon and A.V. Mikhailov, ``Transient Raman Amplification'', ed. V.E. Zakharov and S. Wabnitz, in book ``Optical Solitons: Theoretical challenges and Industrial Perspectives'', pp 265-282, Berlin, Heidelberg; Springer, 1999

  20. S.K. Turitsyn and A.V. Mikhailov, ``Application of soloitons'', ed. R. Pike and P.Sabatier, in book ``Scattering'', Academic Press, pp 1741-1753, 2001.

  21. Mikhailov A, Novikov V, Wang J,”Symbolic representation and classification of integrable systems”. In “Algebraic Theory of Differential Equations”. Editors: MacCallum MAH, Mikhailov AV. 156-216. Cambridge University Press,

  22. Mikhailov A,”Introduction”,In “Integrability”. Editors: Mikhailov AV. 1-18. Springer, Berlin, Heidelberg 2009

  23. Mikhailov A, Sokolov V,”Symmetries of Differential Equations and the problem of Integrability”. In “Integrability”. Editors: Mikhailov AV. 19-88. Springer, Berlin, Heidelberg 2009

    Papers in Refereed Journals

  24. E.A. Kuznetsov and A.V. Mikhailov, ``Stability of Stationary Waves in Nonlinear Weak-dispersive Media'', Journal of Experimental and Theoretical Physics, V.67, p.1717-1727, 1974

  25. A.V. Mikhailov, ``Integrability of the Two Dimensional Thirring Model'', Letters in Journal of Experimental and Theoretical Physics, v.23, p.356-358, 1976

  26. E.A. Kuznetsov and A.V. Mikhailov, ``On the Compete Integrability of the Two Dimensional Classical Thirring Model'', Theoretical and Mathematical Physics, v.30, p. 303, 1977,

  27. V.E. Zakharov and A.V. Mikhailov, ``An Example of Nontrivial Interection of Solitons in Two-dimensional Field Theory'', Letters in Journal of Experimental and Theoretical Physics v.27, p. 47, 1978

  28. V.S. L 'vov and A.V. Mikhailov, ``Sound and Hydrodynamic Turbulence in a Compressible Liquid'', Journal of Experimental and Theoretical Physics, v.74, 1445 - 1457, 1978

  29. V.E. Zakharov and A.V. Mikhailov, ``Relativistically Invariant Models of Field Theory, Integrable by Inverse Transform Method'', Journal of Experimental and Theoretical Physics, v.74, pp. 1953-1973, 1978

  30. V.S. L 'vov and A.V. Mikhailov, ``Scattering and Interaction of Sound in Turbulence'', Journal of Experimental and Theoretical Physics, v.75, pp. 1669-1682, 1978

  31. A.V. Mikhailov, ``Integrability of Supersymmetric Generalization of the Classical Chiral Model in Two-dimensional Space-time'', Letters in Journal of Experimental and Theoretical Physics, v.28, pp. 554-558, 1978

  32. A.V. Mikhailov and A.M. Perelomov, ``Instanton like Solutions for Supersymmetric Chiral Model'', Journal of Experimental and Theoretical Physics Letters, v.29, p. 445, 1979

  33. A.V. Mikhailov, ``On the Integrability of two-dimensional Generalization of the Toda Lattice'', Letters in Journal of Experimental and Theoretical Physics, v.30, p. 443-448, 1979

  34. V.E. Zakharov and A.V. Mikhailov, ``The Variational Principle for Equations Itegrable by the Inverse Transform Method'', Functional Analysis and Its Application, v.14, pp. 55-56, 1980

  35. A.V. Mikhailov and V.E. Zakharov, ``On the Integrability of Classical Spinor Models in Two Dimensional Space-time'', Communications in Mathematical Physics, v.74, p. 21-40, 1980

  36. E.A. Kuznetsov and A.V. Mikhailov, ``On the Topological Meaning of the Classical Clebcsh Variables'', Physics Letters, v.77A, p.37-38, 1980

  37. A.V. Mikhailov, ``Reductions in Integrable Systems. The Reduction Groups.'', Letters in Journal of Experimental and Theoretical Physics, v.32, pp. 187-192, 1980

  38. V.S. L 'vov and A.V. Mikhailov, ``Contribution to the Nonlinear Theory of Sound and Hydrodynamic Turbulence of a Compressible Liquid'', Physica 2D, 224-243, 1981

  39. A.V. Mikhailov, ``Reduction Problem and the Inverse Scattering method'', Physica 3D, N1&2, p73-117, 1981

  40. A.V. Mikhailov, M.A. Olshanetskii and A.M. Perelomov, ``Two Dimensional Generalized Toda Lattice'', Communications in Mathematical Physics, v.79, p. 473, 1981

  41. A.V. Mikhailov and A.I. Yaremchuk, ``Cylindrically Symmetric Solutions of the Non-linear Chiral Model ( - model)'', Nuclear Physics, B202, p. 508-522, 1982

  42. A.V. Mikhailov and A.I. Yaremchuk, ``The Axially Symmetric Solutions of the Two-dimensional Heisenberg model'', Letters in Journal of Experimental and Theoretical Physics, v.36, p78-84, 1982

  43. A.V. Mikhailov, ``The Landau-Lifschitz Equation and the Riemann Boundary Problem on a Torus'', Physics Letters A92, p.51, 1982

  44. I.R. Gabitov, V.E. Zakharov and A.V. Mikhailov, ``On the Shape of the Superfluorescence Pulse'', Letters in Journal of Experimental and Theoretical Physics, v.37, p. 234 - 237, 1983

  45. V.E. Zakharov and A.V. Mikhailov, ``The Inverse Scattering Method with the Spectral Parameter on Algebraic Curves'', Functional Analisis and Its Applications, v.17, p. 1-6, 1983

  46. I.R. Gabitov, V.E. Zakharov and A.V. Mikhailov, ``Non-linear Theory of the Superfluorescence'', Journal of Experimental and Theoretical Physics, v.86, pp. 1204-1216, 1984

  47. A.V. Mikhailov and A.I. Yaremchuk, ``The Forced Motion of a Domain Wall in the Field of a Spin-wave'', Letters in Journal of Experimental and Theoretical Physics, v.39, p. 296-299, 1984

  48. I.R. Gabitov, V.E. Zakharov and A.V. Mikhailov, ``The Maxwell-Bloch Equation and the Inverse Scattering Method'', Theoretical and Mathematical Physics, v.63, pp. 11-31, 1985

  49. A.V. Mikhailov and A.B. Shabat, ``The Integrability Conditions for the System of two Equations of the form . I'', Theoretical and Mathematical Physics, v.62, pp. 163-185, 1985

  50. A.V. Mikhailov and A.B. Shabat, ``The Integrability Conditions for the System of two Equations of the form . II'', Theoretical and Mathematical Physics, v.66, pp. 47-65, 1986

  51. A.V. Mikhailov and A.B. Shabat, ``Integrable Deformations of the Heisenberg model'', Physics Letters, A116, pp. 191-194, 1986

  52. S.P. Burtsev, V.E. Zakharov and A.V. Mikhailov, ``The Inverse Scattering Method with Variable Spectral Parameter'', Theoretical and Mathematical Physics, v.70, p.232-241, 1987

  53. A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, ``On an Extansion of the Module of Invertible Transformations'', Soviet Mathematical Doklady (Soviet Mathematical Surveis) , v.295, pp. 288-291, 1987

  54. A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, ``The Symmetry Approach to the Classification of Non-linear Equations. Complete Lists of Integrable Systems'', Soviet Mathematical Doklady (Soviet Mathematical Surveis), v.42, pp. 3-53, 1987

  55. V.E. Zakharov and A.V. Mikhailov, ``Domains of Polarization in Nonlinear Optics'', Letters in Journal of Experimental and Theoretical Physics v.45, p.279-282, 1987

  56. A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, ``Extension of the Module of Invertible Transformations and Classification of Integrable Systems'', Communications in Mathematical Physics, v.115, pp. 1-19, 1988

  57. A.V. Mikhailov and S. Wabnitz, ``Polarization Dynamics of Counterpropogating Beams in Optical Fibers'', Optics Letters, v.15, pp. 1055-1057, 1990

  58. A.V. Mikhailov and I.A. Shimokhin, ``Excitation Spectrum of a Domain wall in Uniaxial Ferromagnets'', Journal of Experimental and Theoretical Physics, 97, 1966, 1990

  59. A.V. Mikhailov, H.J. de Vega and N. Sánchez, ``Exact String Solutions in 2+1 - Dimensional de Sitter Spacetime'' Theoretical and Mathathematical Physics, v. 94, pp. 232, 1993

  60. A.V. Mikhailov and I.A. Shimokhin, ``Spectrum of Bloch-Type Domain Wall Excitations in Yttrium Iron Garnet'', Physical Reveiw B, v. 48, N13 pp. 9569-9674, 1993

  61. F. Combes, A.V. Mikhailov, H.J. de Vega and N.Sánchez,``Multi-String Solutions by Soliton Methods in de Sitter Spacetime'' Physical Reveiw D, 30, N 4, pp. 2754-2768, 1994

  62. E.A. Kuznetsov and A.V. Mikhailov, ``Relaxation Oscillations of Solitons'' Letters in Journal of Experimental and Theoretical Physics, v. 60, pp. 466-470, 1994

  63. E.A. Kuznetsov, A.V. Mikhailov and I.A. Shimokhin, ``Nonlinear Interaction of Solitons and a Radiation'' Physica D, v. 87, pp. 201-215, 1995

  64. C. Montes, A.V. Mikhailov, A. Picozzi and F. Ginovart, ``Dissipative 3-wave Structures Stimulated Backscattering: I. Sub-Luminous solitary attractor'', Physical Reveiw E, v55, pp. 1086-1091, 1997

  65. A.V. Mikhailov and R.I. Yamilov, ``On Integrable two-dimensional generalisations of Nonlinear Schrödinger type Equations'' Physics Letters A, 230, pp. 295-300, 1997

  66. Y. Kodama, A.V. Mikhailov and S. Wabnitz, ``Input pulse optimization in wavelength-division-multiplexed soliton transmissions'', Journal of Optics Communicatons, 143/1-3, pp. 53-56, 1997

  67. A.V. Mikhailov and R.I. Yamilov, ``Towards Classification of 2+1 dimensional Integrable Equations. Integrability conditions I'', Journal of Physics A, 31, pp. 6707-6715, 1998.

  68. J. Leon and A.V. Mikhailov, ``Raman Soliton Generation from Laser Inputs in SRS'', Physics Letters A, 253, pp, 33-40, 1999

  69. A.V. Mikhailov and V.V. Sokolov, ``Integrable evolutionary equations on free associative algebras'', Journal of Theoretical and Mathematical Physics (TMF), 122, pp 72-83, 2000.

  70. A.V. Mikhailov and V.V. Sokolov, ``Integrable ODEs on Associative Algebras'', Communications in Mathematical Physics, 211, pp. 231-251, 2000.

  71. Y. Kodama and A.V. Mikhailov, ``Symmetry and perturbation of the vector nonlinear Schrödinger equation '', Physica D 152-153, pp 171-177, 2001.

  72. A.V. Mikhailov, V.Yu. Novokshenov, ``The Period Map for Pulse Propagation in Nonlinear Optical DM Fibres'', JETP Letters, Vol. 73, No. 5, pp. 250-254, 2001.

  73. A.V. Mikhailov, V.S. Novikov, ``Perturbative symmetry approach''. J. Phys. A 35, no. 22, 4775-4790, 2002.

  74. A.V. Mikhailov, V.S. Novikov, Classification of integrable Benjamin-Ono-type equations. Moscow Mathematical Journal 3, no. 4, 1293-1305, 2003.

  75. A.V. Mikhailov, V.Yu. Novokshenov, ``Period Map for Nonlinear Pulses in Optical Dispersion-Managed Fibres'', Theoretical and Mathematical Physics, 134, no 1, pp. 107-116, 2003.

  76. S. Lombardo, A.V. Mikhailov. ``Reductions of integrable equations: dihedral group''. J. Phys. A 37, no. 31, 7727-7742, 2004.

  77. S. Lombardo, A.V. Mikhailov ``Reduction groups and Automorphic Lie Algebras''. Communication in Mathematical Physics, (2005), published electronically in March (DOI: 10.1007/s00220-005-1334-5), 258, no. 1, pp. 179-202, 2005.

  78. A.V. Mikhailov, V.S. Novikov and J.P. Wang, ``Partially integrable nonlinear equations with one higher symmetry'', J. Phys. A: Math. Gen. 38, L337-L341, 2005.

  79. Mikhailov AV, Novikov VS, Wang JP, “On classification of integrable nonevolutionary equations”,STUD APPL MATH 118(4):419-457 May 2007

  80. Gerdjikov VS, Mikhailov AV, Valchev TI,”Reductions of integrable equations on A.III-type symmetric spaces”, J PHYS A-MATH THEOR 43(43): Article number 434015 29 Oct 2010

  81. 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

  82. Mikhailov AV, Wang JP, Xenitidis P.“Recursion operators, conservation laws, and integrability conditions for difference equations”,Theoretical and Mathematical Physics 167(1):421-443 Apr 2011

  83. 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 (2011), no. 3, 740 - 750 09 Feb 2011

  84. Mikhailov AV, Wang JP, Xenitidis P, “Cosymmetries and Nijenhuis recursion operators for difference equations”, NONLINEARITY 24(7):2079-2097 Jul 2011

  85. Gerdjikov VS, Grahovski GG, Mikhailov AV, Valchev TI,”Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces”,SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 7 Oct 2011

  86. Mikhailov AV, Wang JP,”A new recursion operator for Adler’s equation in the Viallet form”, Physics Letters A 375:3960-3963 21 Sep 2011


               Preprints

  87. Bhatt R, Mikhailov AV,”On the inconsistency of the Camassa-Holm model with the shallow water theory”, http://arxiv.org/pdf/1010.1932v1


               Other


  88. A.A. Galeev, E.A. Kuznetsov, A.V. Mikhailov, Yu.E. Nesterikhin, S.P. Novikov, R.Z. Sagdeev, Ya.G. Sinai, G.I. Smirnov, V.E. Fortov, I.M. Khalatnikov, B.V. Chirikov, A.B. Shabat," Vladimir Evgen'evich Zakharov (on his sixtieth birthday)" ,Physics Uspekhi, Volume 42, Number 10, Pages 1063-1064, 1999.








AVM 2011/10/28