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The World of Mathematical Equations

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Nikolai A. Kudryashov   

Nikolai A. Kudryashov

Prof., PhD, Sc.Dr.
Head of Department of Applied Mathematics

Born: September 19, 1945, Russia

Education and Degrees:

  • M.S. in Theoret. and Math. Physics, March 3, 1974, Moscow Engineering Physics Institute
  • Ph. D. in math. Physics, November 13, 1978 Moscow Engineering Physics Institute
  • Doctor of Sciences in Mathemat. Physics, April 2, 1986, Moscow Engineering Physics Institute

Current Professional Status:

  • Head of Department of Applied Mathematics of Moscow Engineering Physics Institute, Moscow, Russia;

Memberships and awards:

  • State Prize Laureate of USSR, Soros Professor, Meritorious Science Worker of the Russian Federation, Academician of the Russian Academy of Natural Sciences
  • Grant Holder and Colaborator of:
    • Soros Educational program
    • International Science and Technology Center (ISTC)
    • US Civilian Research and Development Foundation
    • Russian Foundation for Basic Research
  • Editorial Board of the website EqWorld: The World of Mathematical Equations (http://eqworld.ipmnet.ru);

Research interests:

  1. Theory of Ordinary and Partial Differential Equations (ODEs and PDEs)
    • Integrable and nonintegrable models, Painleve analysis of nonlinear differential equations
    • Analytical exact solutions for nonlinear PDEs
    • Conservation laws and first integrals
    • Local and nonlocal symmetries and transformations for ODEs and PDEs
    • Solitons and self-similar solutions
  2. Mathematical Modelling of nonlinear waves processes
    • Continuum mechanics, Fluid and gas dynamics
    • Biophysics (Hemodynamics) and symbolical sequences
    • Ecology and Earth sciences (modelling of volcanoes and tsunamis)
  3. Numerical methods
    • Difference equations
    • Finite-difference and spectral schemes, finite element methods
    • Application to modelling of nonlinear wave processes

Teaching courses:

  • Mathematical problems in Hydrogasodynamics
  • Nonlinear problems of mathematical physics
  • Introduction to nonlinear dynamics
  • Lie groups for ODEs
  • Finite-Difference Methods
  • Partial Differential Equations for Scientists and Engineers
  • Intoduction to solitons

Selected Publications:

  1. Nikolai A. Kudryashov, Seven common errors in finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, (2009), V. 14, I. 9-10, pp. 3507-3529
  2. Nikolai A. Kudryashov, On "new travelling wave solutions" of the KdV and the KdV-Burgers equations, Communications in Nonlinear Science and Numerical Simulation, (2009), V.14, I.5, pp. 1891-1900
  3. Nikolai A. Kudryashov, Nadejda B. Loguinova, Be careful with the Exp-function method, Communications in Nonlinear Science and Numerical Simulation, (2009), V.14, I.5 pp. 1881-189
  4. Nikolai A. Kudryashov, Special polynomials associated with rational solutions of some hierarchies, Chaos, Solitons & Fractals, (2009), V. 39, I. 3, pp. 1447-1462
  5. Nikolai A. Kudryashov, Nadejda B. Loguinova, Extended simplest equation method for nonlinear differential equations, Applied Mathematics and Computation, (2008), V. 205, I. 1, pp. 396-402
  6. Nikolai A. Kudryashov, Maria V. Demina, The generalized Yablonskii-Vorob'ev polynomials and their properties, Physics Letters A, (2008), V. 372, I. 29, pp. 4885-4890
  7. Demina, M.V., Kudryashov, N.A., Sinel'Shchikov, D.I. The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves, Computational Mathematics and Mathematical Physics, (2008), V. 48 (12), pp. 2182-2193
  8. Kudryashov, N.A., Demina, M.V., Relations between zeros of special polynomials associated with the Painleve equations, Physics Letters A,(2007), V. 368, I. 3-4, pp. 227-234.
  9. Kudryashov, N.A., Demina, M.V., Polygons of differential equations for finding exact solutions, Chaos, Solitons and Fractals, (2007), V. 33, I. 5, pp. 1480-1496.
  10. Demina, M.V., Kudryashov, N.A., The Yablonskii-Vorob'ev polynomials for the second Painleve hierarchy, Chaos, Solitons and Fractals,(2007), 32 (2), pp. 526-537.
  11. Kudryashov, N.A., Efimova, O.Yu., Power expansions for solution of the fourth-order analog to the first Painleve equation, Chaos, Solitons and Fractals, (2006) , 30 (1), pp. 110-124
  12. N.A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, (2005), 24, pp.1217-1231
  13. N.A. Kudryashov, Fuchs indices and the first integrals of nonlinear differential equations, Chaos, Solitons and Fractals, (2005), v.26, No.2
  14. N.A. Kudryashov, Nonlinear differential equations with exact solutions expressed via the Weierstrass function, Zeitschrift fur Naturforschung, (2004), v.59
  15. E.V.Korotkov, M.A.Korotkova, N.A. Kudryashov, Information decomposition method to analyze the symbolical sequences, Physics Letters A, (2003), v.312, 3-4, pp.198-310
  16. E.V. Korotkov, M.A. Korotkova, F.E. Frenkel, N.A. Kudryashov, The Informational Concept of Searching for Periodicity in Symbol Sequences, Molecular Biology, (2003), Vol.37, No.3, pp.372-386.
  17. M.B. Chaley, E.V. Korotkov, N.A. Kudryashov, Latent periodicity of 21 bases typical for MCP, Gene is widely present in various bacterial genes, DNA sequences, (2003), vol.14(1), pp.33-52
  18. N.A. Kudryashov, Amalgamations of the Painlevé equations, Journal of Math. Physics, (2003), v.44, 12
  19. N.A. Kudryashov, Fourth-order analogies to the Painleve equations, Journal of Physics A.: Math. General, (2002), v.35, pp.4617-4632
  20. N.A. Kudryashov, One Generalization of the second Painleve hierarchy, Journal of Physics A: Math. General, (2002), v.35, pp.93-99
  21. N.A. Kudryashov, M.B. Soukharev, Descrete equations corresponding to fourth-order differential equations of the P2 and K2 Hierarchies, Proceedings ANZIAM, Journal of Industrial and Applied Mathematics, (2002)
  22. N.A. Kudryashov, Some fourth ordinary differential equations which pass the Painleve test, Journal of Nonlinear Mathematical Physics, (2001), v.8, Supplement, Proceedinds:Needs 99
  23. N.A. Kudryashov, Double Backlund transformations and special integrals for the K II hierarchy, Physics Letters A, (2000), v.273, pp.194-202
  24. N.A. Kudryashov, Two hierarchies of ordinary differential equations and their properties, Physics Letters A, (1999), 252, pp.173-179
  25. N.A. Kudryashov, Transcendents defined by nonlinear fourth order differential equations, Journal of Physics A: Math. and General, (1999), v.32, 6, pp.999-1014
  26. N.A. Kudryashov, S.N. Kolobanov, Numerical modeling of the distribution of radionuclides in porous media at strong damage of undeground nuclear power station, International Journal of Heat and Mass Transfer, (1999), 42, pp.3695-3705.
  27. S.A. Chesnokov, N.A. Kudryashov, Yu.I. Sytsko, Numerical modeling of gravitational waves behaviour in the ocean with a shallow water approximation, Journal of Engineering Physics, (1999), v.72, No.6, pp.1180-1186 (in russian)
  28. N.A. Kudryashov, M.B. Soukharev, Uniformization and Transcendence of solutions for the first and second Painleve hierarchies, Physycs Letters A, (1998), v.237, pp.206-216
  29. N.A. Kudryashov, A. Pickering, Rational solutions for Schwarzian integrable hierarchies, Journal of Physics A: Math. and General, (1998), v.31, No.47, pp.9505-9518
  30. N.A. Kudryashov, On new transcendents defined by nonlinear ordinary differential equations, Journal of Physics A: Math. and General, (1998), v.31, No.6, pp.L129-L137
  31. N.A. Kudryashov, The first and the second Painleve equations of higher order and some relations between them, Physics Letters A, (1997), v.224, pp.353-360
  32. N.A. Kudryashov, The second Painleve equation as the model of electric field in a semiconductor, Physics Letters A, (1997), v.233, pp.397-400
  33. N.A. Kudryashov, Method for Deriving Rational Solutions of Some Nonlinear Evolution Equations, Journal of Physics A: Math. and General, (1997), v.30, pp.5445-5453
  34. N.A. Kudryashov, E.D. Zargaryan, Solitary waves in active-dissipative dispersive media, Journal of Physics A: Mathematical and General, (1996), v.29, No.24, pp.8067-8077
  35. N.A. Kudryashov, From singular manifold equations to integrable evolution equation, Journal of Physics A: Mathematical and General, (1994), v.27, No.4, pp.2457-2470
  36. N.A. Kudryashov, Singular manifold exations and exact solutions for some nonlinear partial differential equations, Physics Letters A, (1993), vol.182, No.4-6, pp.356-362
  37. N.A. Kudryashov, Truncated expansions and nonlinear integrable partial differential equations, Physics Letters A, (1993), vol.178, No.1-2, pp.99-104
  38. N.A. Kudryashov, Partial differential equations with solutions having movable first-order singularities, Physics Letters A, (1992), vol.169, No.4, pp.237-242
  39. S.S. Kucherenko, N.A. Kudryashov, Photoelectric characteristics of a semiconductor diode with an abrupt junction at high photoexcitation levels, Solid-State Electronics, (1992), Vol.35, No.7, pp.993-997
  40. N.A. Kudryashov, On types of nonlinear nonintegrable equations with exact solutions, Physics Letters A, (1991), vol.155, No.4-5, pp.269-275
  41. V.A. Arutyunov, N.A. Kudryashov, O.A. Mishin V.M. Samsonov, M.N. Strikhanov, Radiactive polarization of relativistic lepton beams in a bent crystals, Physics Letters A, (1991), vol.151, No.1-2, pp.122-124
  42. V.A. Arutyunov , N.A. Kudryashov, V.M. Samsonov, M.N. Strikhanov, Channeling radiation in a bent crystals, Physics Letters A, (1991), vol.151, No.9, pp.481-484
  43. V.A. Arutyunov, N.A. Kudryashov, M.N. Strikhanov, Radiation of Ultrarelatistic Charged Particles in a Bent Crystal, Nuclear Physics B, (1991), 263, p.283
  44. A.A. Alexeyev, N.A. Kudryashov, Non-abelian pseudopotentials and conservation laws of reaction-diffusion equations, Journal of Physics A: Mathematical and General, (1991), vol.24, No.6, pp.L255-L260
  45. N.A. Kudryashov, Exact solutions of generalized Kuramoto-Sivashinsky equation, Physics Letters A, (1990), vol.147, No.5-6, pp.287-291
  46. V.A. Arutyunov, N.A. Kudryashov, O.A. Mishin, V.M. Samsonov, M.N. Strikhanov, Radiative polarization effects for relativistic beams in bent crystals, Nuclear Instruments and Methods in Physics Research B, (1990), 52, pp.13-18
  47. N.A. Kudryashov, S.V. Petrovsky, V.M. Samsonov, M.N. Strikhanov, Energy Loss Distribution of Relativistic Charged Particls in Crystals, Physica status solidi (b), (1990), vol.157, No.2, pp.531-545
  48. N.A. Kudryashov, Exact soliton solutions of the generalized evolution equation of wave dynamics, Prikladnaya Mathematica i Mechanika, (1988), vol.52, No.3, pp.465-470 (translated from russian)

Mailing Address:

Room K-1106, Department of Applied Mathematics at Moscow Engineering and Physics Institute (MEPhI),
31 Kashirskoe shosse,
Moscow 115409, Russian Federation

E-mail: kudryashov@mephi.ru
Home page: http://www.primat.mephi.ru/~kudryashov/

Page last updated: 3 July 2009 Main page of the EqWorld website