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Depart ment of Mathematical Physics

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Scientific Interests
Experience
Conferences
Publications

About the Department

Viktor Yurievich Novokshenov

Head of the Department of Differential Equations,
Doctor of Science, Professor

Scientific Interests

  • Nonlinear mathematical physics

Experience

  • Place of birth - (1951) Sverdlovsk, Russia
  • 1969 Graduated from high school. Sverdlovsk, Russia
  • 1969-1974 Department of Mathematics and Mechanics, Urals State University, Sverdlovsk, Russia. B.S.Degree, 1974
  • 1974-1978 Institute of Mathematics, Bashkir Branch of the Academy of Sciences of the USSR, Ufa. Ph.D. Degree, March 1979 (supervisor Prof. A.M.Il'in)
  • 1988 Second Phys.-Math.D. Degree at Leningrad Branch of Steklov Mathematical Institute (title: Isomonodromic Deformations and Painleve Equations)
  • 1978-1981 Junior Researcher in Institute of Mathematics, Bashkir Branch of the Academy of Sciences, Ufa, Russia; from 1981 Senior Researcher, from 1988 Leading Researcher
  • Today Head of the Department of Mathematical Physics, Institute of Mathematics, Ufa Scientific Center of RAS
  • For many years gives the lecture courses in USATU and BSU

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Conferences

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Publications

Journals

  • [1.] V.Yu.Novokshenov Asymptotics of the Solution of an Elliptic Equation with Discontinuous Boundary conditions, Differential Equations, 12, N 10, p.1625-1637 (1976).
  • [2.]V.Yu.Novokshenov Asymptotics of the Solution for the Singular Integral Equation with Small Parameter, Matem. Sbornik, 100 , N 3, p.455-475 (1976).
  • [3.] V.Yu.Novokshenov Singular Integral Equation with Small Parameter on a Finite Interval, Matem.Sbornik, 105 , N 4,p.543-573 (1978).
  • [4.] V.Yu.Novokshenov Convolution Equation on a Finite Interval and Factorization of Elliptic Matrices, Matem. Zametki, 27 , N 6, p.935-946 (1980).
  • [5.] V.Yu.Novokshenov Small Parameter Asymptotics of the Solution for Elliptic Pseudodifferential Equation in a Half-space, "Differential Equations with Small Parameter", Sverdlovsk, p.87-111, (1980).
  • [6.] V.Yu.Novokshenov Asymptotics as t ® Ґ of the Solution of the Cauchy Problem for Nonlinear Schrodinger Equation, Doklady AN SSSR, 251 , N 4, p.799-801 (1980).
  • [7.] V.Yu.Novokshenov, I.T.Habibullin Nonlinear Differential -Difference Schemes, Integrable by the Inverse Scattering Method, Doklady AN SSSR, 257 , N 3, p.543-547 (1981).
  • [8.] V.Yu.Novokshenov, Sh.H.Khannanov The Kinetics of the Intercrystalline Crack Development Caused by a Diffusion Mass-Transfer, Applied Mechanics and Technical Phisics, N 3,p.136-141 (1981).
  • [9.] V.Yu.Novokshenov Asymptotic Formulae for the Solutions of the System of Nonlinear Schrodinger Equations, Uspekhi Matem. Nauk, 37 , N 2, p.215-216 (1982).
  • [10.] V.Yu.Novokshenov Asymptotics as t ® Ґ of the Solution to a Two-Dimentional Generalisation of the Toda Lattice, Doklady AN SSSR, 265 , N 6, p.1320-1324 (1982) (Soviet Math. Dokl. 26, N 1, 264-268 (1982).)
  • [11.] V.Yu.Novokshenov Asymptotics of solution for discrete nonlinear Schrodinger equation and its continuous limit, Ïntegrablr Systems", Ufa, p.49-52 (1982)
  • [12.] V.Yu.Novokshenov Asymptotic Behavior as t ®Ґ for the Solution of the Cauchy Problem for Nonlinear Differential-Difference Schrodinger Equation , Differential Equations, 21, N 11, p. 1915-1926 (1985).
  • [13.] V.Yu.Novokshenov, Sh.H.Khannanov Dislocation Model and Kinetics of High - Temperatire Grain Slipping on the Boundary , Physics of Metals, 57, N 5, p.1015-1020 (1984).
  • [14.] V.Yu.Novokshenov, I.T.Habibullin Asymptotic Behavior of Differential-Difference Wave Systems Integrable by the Inverse Scattering Method, Proceedings of S.L.Sobolev Seminar, N 2, p.10-53 (1982).
  • [15.] V.Yu.Novokshenov Asymptotics of the Solution of Discrete Nonlinear Schrodinger Equation and its Continuons Limit, Integrable Systems", ed. A.B.Shabat, p.49-52, Ufa (1982).
  • [16.] V.Yu.Novokshenov Asymptotics as t ® Ґ of the Solution of the Canchy Problem for Two-Dimensional Toda Lattice, Izvestia AN SSSR, math. ser., 48 , N 2, p.372 - 410, (1984).
  • [17.] V.Yu.Novokshenov The Method of Isomonodromic Deformation and Asymtotics of the Third Painleve Transcendent, Funktsional Anal. i Prilozhen. 18 , N 3, p.90-91 (1984).
  • [18.] D.N.Gainanov, V.Yu.Novokshenov, L.I.Tyagunov On the Graphs Generated by Inconsistent Systems of Linear Inequalities, Matem. Zametki, 33 , N 2, p.293-300 (1983).
  • [19.] V.Yu.Novokshenov On the Asymptotics of General Real- Valued Solution of the Third Painleve Equation, Doklady AN SSSR, 283 , N 5, p.1161-1165 (1985).
  • [20.] S.V.Manakov, V.Yu.Novokshenov The Complete Asymptotic Representation of Electromagnetic Impulse in a Long Laser Amplifyer, Teoret. Matem.Fiz. 69 , N 1, p.40-54 (1986).
  • [21.] V.Yu.Novokshenov Movable Poles of the Third Painleve Transcendents and their Interrelations with the Mathieu Functions, Funktsional Anal. i Prilozhen. 20 , N 2, p.38 - 49 (1986).
  • [22.] A.A.Kapaev, V.Yu.Novokshenov Two-Parameter Family of Real-Valued Solutions of the Second Painleve Equation, Doklady AN SSSR, 290 , N 3,p.590-594 (1986).
  • [23.] V.Yu.Novokshenov Quasiclassical Mode of Three -Dimensional Wave Collapse and the Asymptotics of Painleve Functions, Uspekhi Matem.Nauk, 41 , N 4,p.170 (1986).
  • [24.] A.R.Its, V.Yu.Novokshenov On the Effective Sufficient Conditions of Solvability of Monodromy Inverse Problem for a System of Ordinary Differential Equations, Funktsional Anal.i Prilozhen., 22 , N 3, p.25-36 (1988).
  • [25]A.R.Its, A.G. Izergin, V.E. Korepin, V.Yu. Novokshenov, Temperature autocorrelations of the transverse Ising chain at the critical magnetic field, Preprint ITP-SB-89-96 of Inst. Theor. Phys. at Stony Brook, 1989.
  • [26.] R.F.Bikbaev, V.Yu.Novokshenov The Korteveg-de Vries Equation with Finite Gap Boundary Conditions and Self-Similar Solutions of Whitham Equations, Proc. III International Workshop "Nonlinear and Turbulent Processes in Physics", Kiev, Vol.1, p.32-35 (1988).
  • [27.] R.F.Bikbaev, V.Yu.Novokshenov On existence and uniquness of solution for Whitham equations, Äsymptotic Methods of Mathematical Physics", Ufa, p. 81-95, (1989).
  • [28.] V.Yu.Novokshenov Modulated Elliptic Function as a Solution of the Second Painleve Equation in the Complex Plane, Doklady AN SSSR, 311 , N 2, p.288-291 (1990).
  • [29.] V.Yu.Novokshenov The Boutroux Ansatz for the second Painleve equation in a complex plane, Izvestia AN SSSR, math. ser. 54 , N 6, p.1229-1251 (1990).
  • [30.] V.Yu.Novokshenov Nonlinear Stokes Phenomenon for the second Painleve equation, Physica 63D , 1& 2, p.1-7 (1993).
  • [31.] V.Yu.Novokshenov Reflectionless Potentials and Soliton Series of the KdV Equation, Teor. Mat. Fiz., 93 , N 2, p.286-301 (1992).
  • [32.] V.Yu.Novokshenov Whitham Deformations of the Top-like Integrable Dynamical Systems, Funkts.Analiz i ego prilozh., 27 N 2, p.50-62 (1993).
  • [33.] A.S.Fokas, A.R.Its and V.Yu.Novokshenov Integrable Equations with Forcing of a Distribution Type, Studies in Appl. Math. XCII , N 2, p.97-114 (1994).
  • [34.] Novokshenov V.Yu. Singular solutions of the cosh-Laplace equation, SFB 288 Preprint # 64, Berlin TU (1993).
  • [35.] Novokshenov V.Yu. Modulated solutions of the Sine-Gordon equation with finite-gap boundary conditions , SFB 288 Preprint # 62, Berlin TU (1993).
  • [36.] Novokshenov V.Yu. Reflectionless Potentials and Soliton Series of the Nonlinear Schrödinger Equation, Physica D, v.87 (1995) p.101-106.
  • [37]V.Yu.Novokshenov, Breather-train solution of the Sine-Gordon equation with "periodic wave - zero" boundary conditions, Asymptotic Analysis, 1996, V.12 p.77-89.
  • [38]V.Yu.Novokshenov, Minimal surfaces in the hyperbolic space and radial-symmetric solutions of the cosh-Laplace equation, in Algebraic and Geometric Methods in Mathematical Physics", eds. A.Boutet de Monvel and V.Marchenko, Kluwer Academic Publishers, 1996, p.357-370.
  • [39] V.Yu.Novokshenov, Dynamics of the Whitham gaps for real-valued solutions of Sine-Gordon equation with finite-gap boundary conditions, Funct. Analiz i ego prilozh., 1996, Т.30, No 4, С.31-44.
  • [40]V.Yu.Novokshenov, A.G.Shagalov, Bound states for the elliptic sine-Gordon equation, Physica D, v.106 (1997) p.81-94
  • [41]V.Yu. Novokshenov, Radial-Symmetric Solution of the Cosh-Laplace Equation and the Distribution of Its Singlarities, Russian. J. Math. Phys., v.5, N 2 1998, 211-226.

Monography

  • [1.] A.R.Its, V.Yu.Novokshenov The Isomonodromic Deformation Method in the Theory of Painleve equations. Lecture Notes in Mathematics, Vol. 1191, 313 p. Springer-Verlag. (1986).

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V.Yu. Novokshenov