Head of Department of Applied Mathematics
In russian
Professor Nikolai A. Kudryashov, Ph.D., D.Sc.
Contact information
Address: Room K-1106, Department of Applied Mathematics at Moscow Engineering and Physics Institute (MEPhI), 31 Kashirskoe shosse, Moscow 115409, Russian Federation
Tel.: +7(495)324-11-81
Fax.: +7(495)324-11-81
E-mail: kudryashovmephi.ru
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
Research interests
  1. Theory of Ordinary and Partial Differential Equations (ODEs and PDEs)
    • Integrable and nonintegrable models, Painlevå 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 papers ( Full list of publications )
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
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
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
Nikolai A. Kudryashov, Special polynomials associated with rational solutions of some hierarchies, Chaos, Solitons & Fractals, (2009), V. 39, I. 3, pp. 1447-1462
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
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
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
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.
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.
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.
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
N.A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, (2005), 24, pp.1217–1231
N.A. Kudryashov, Fuchs indices and the first integrals of nonlinear differential equations, Chaos, Solitons and Fractals, (2005), v.26, No.2
N.A. Kudryashov, Nonlinear differential equations with exact solutions expressed via the Weierstrass function, Zeitschrift fur Naturforschung, (2004), v.59
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
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.
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
N.A. Kudryashov, Amalgamations of the Painlevé equations, Journal of Math. Physics, (2003), v.44, 12
N.A. Kudryashov, Fourth-order analogies to the Painleve equations, Journal of Physics A.: Math. General, (2002), v.35, pp.4617-4632
N.A. Kudryashov, One Generalization of the second Painleve hierarchy, Journal of Physics A: Math. General, (2002), v.35, pp.93-99
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)
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
N.A. Kudryashov, Double Backlund transformations and special integrals for the K II hierarchy, Physics Letters A, (2000), v.273, pp.194–202
N.A. Kudryashov, Two hierarchies of ordinary differential equations and their properties,
Physics Letters A, (1999), 252, pp.173-179
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
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.
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)
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
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
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
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
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
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
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
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
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
N.A. Kudryashov, Truncated expansions and nonlinear integrable partial differential equations, Physics Letters A, (1993), vol.178, No.1-2, pp.99-104
N.A. Kudryashov, Partial differential equations with solutions having movable first-order singularities, Physics Letters A, (1992), vol.169, No.4, pp.237-242
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
N.A. Kudryashov, On types of nonlinear nonintegrable equations with exact solutions, Physics Letters A, (1991), vol.155, No.4-5, pp.269-275
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
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
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
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
N.A. Kudryashov, Exact solutions of generalized Kuramoto-Sivashinsky equation, Physics Letters A, (1990), vol.147, No.5-6, pp.287-291
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
N.À. Êudryashov, 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
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)