The Department was founded by Arlen Mikhailovich Il'in (today the RAS academician) in 1974. At first it was established as the Sector of Differential Equations in the Department of Physics and Mathematics, the Bashkir Branch of the USSR Academy Of Sciences. When the Institute of Mathematics with Computing Center was organized the Sector was renamed to the Department of Differential Equations. Since 1990 the head of the Department is Professor Leonid Anatolievich Kalyakin.

The main lines of investigation in the Department are the asymptotic methods for studying the solutions of partial and ordinary differential equations, differential equations with a small parameter, singular perturbations of boundary-value and initial problems.

Research

• Autoresonance
• Soliton generation
• Catastrophes and kink generation
• Separatrices and chaos in the solutions of ordinary differential equations

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Seminars

In 2004 researchers of the Department participated in the following international and all-russian conferences:

• 5-9 December, Int. Conf. on Complex analysis, equations of mathematical physics, computational Mathematics, Yaktykul', Russia
• 24 June - 3 July Int. conference "Nonlinear Physics: Theory and Experiment III", Gallipoli, Lecce, Italy (L.A. Kalyakin)
• June, Int. Conf. on Symmetry and Perturbation Theory, Cala-Gonone, Italy (R.N. Garifullin)
• 10-14 May Conference "New mathematical models in mechanics of continua: constructing and studying", Novosibirsk, Russia (Yu.Yu. Bagderina)
• May, Int. Conf. "Differential Equations and Related Topics", Moscow, Russia (R.N. Garifullin, L.A. Kalyakin)

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Teaching

The Department maintains close contacts with the principal Ufa universities:

• Bashkir State University,
• Ufa State Aviation Technical University,
• Ufa State Petroleum Technical University.

In these universities for a long time we give the lecture courses on the principal mathematical topics:

• Ordinary differential equations;
• Partial differential equations;
• Discrete mathematics

• Hamilton mechanics;
• Nonlinear oscillations;
• Special functions;
• Theory and planning of the experiment;
• Numerical-analytic methods.

Also we perform a research with the students and post-graduate students of the above mentioned universities.

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Collaboration

The new research trends and obtained results are discussed with the colleagues from

• Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg;
• Institute for Problems in Mechanics of RAS, Moscow;
• Saint-Petersburg Division of V.A. Steklov Mathematical Institute of RAS, Saint-Petersburg;
• Moscow State University, Moscow;
• Landau Institute for Theoretical Physics of RAS, Moscow;
• B.Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine;
• Dept. of Mathematics, South Methodist University, Dallas, USA;
• Dept. of Mathematics, McMaster University, Canada
• Dept. of Mathematics , University of Cape Town, South Africa
  and other research organizations.

People of this department work in collaration with teams from

• Laboratory of Nonlinear Mechanics, Institute of Metal Physics, Ekaterinburg;
• Department of Theoretical Physics, P.N. Lebedev Physical Institute, Moscow;
• Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Troitsk;
• Department of Nonlinear waves Institute of Applied Physics, Nizhnii Novgorod;
• Department of Optics and Fluid Mechanics, RISOE National Laboratory, and Institute of Mathematical Modeling, The Technical University of Denmark
• Racah Institute of Physics, Hebrew University, Jerusalem, Israel
• University of Bayreuth, Bayreuth, Germany

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Staff

• Kalyakin Leonid Anatolievich
  (Head of the Department)

• Bagderina Yulia Yurievna

• Garifullin Rustem Nailevich

• Kiselev Oleg Mikhailovich

• Suleimanov Bulat Irekovich