EqWorld

The World of Mathematical Equations

Andrei Dmitrievich POLYANIN Ph.D., D.Sc., Professor

Born: 1 November 1951

Education and Degrees:

• M.Sc., 1974, Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University; graduated with honours;
• Ph.D., 1981, Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow;
• D.Sc., 1987, Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow.

Current Professional Status:

• Chief Scientific Officer, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
• Professor (part-time), Department of Fundamental Sciences, Bauman Moscow State Technical University, 2004–2021;
• Professor (part-time), Department of Applied Mathematics, National Research Nuclear University MEPhI, 2014–2020.

Membership:

• Russian National Committee on Theoretical and Applied Mechanics;
• Mathematics and Mechanics Expert Council, Higher Certification Committee, Ministry of Education and Science of the Russian Federation, 2006–2022;
• Editorial Board of the Journal Mathematics;
• Editorial Board of the Journal Theoretical Foundations of Chemical Engineering;
• Editorial Board of the Journal Mathematical Modeling and Numerical Methods (in Russian);
• Editorial Board of the Journal Vestnik Natsional'nogo Issledovatel'skogo Yadernogo Universiteta "MIFI" (in Russian).

Editor:

• Website EqWorld: The World of Mathematical Equations (http://eqworld.ipmnet.ru);
• Website MechMath: The Mechanics and Applied Mathematics (http://mechmath.ipmnet.ru, in Russian);
• Book series Differential and Integral Equations and Their Applications, Chapman & Hall/CRC Press, Boca Raton–London.

Honours, Awards and Prizes:

• Chaplygin Prize of the Russian Academy of Sciences, 1991;
• Award from the Ministry of Education of the Russian Federation, 2001;
• Russian State Scientific Stipend to Outstanding Scientists, 1997–2003.

Areas of Expertise:

• ordinary differential equations, partial differential equations,
• mathematical physics, delay partial differential equations,
• integral equations, functional equations,
• applied and engineering mathematics,
• heat and mass transfer, hydrodynamics,
• chemical engineering sciences.

Author:

• More than 30 books in English, Russian, German, and Bulgarian including several best-selling handbooks;
• more than 270 research papers and three patents.

Books in English

1. A. D. Polyanin, Handbook of Exact Solutions to Mathematical Equations, CRC Press, Boca Raton–London, 2024.
2. A. D. Polyanin, V. G. Sorokin, and A. I. Zhurov, Delay Ordinary and Partial Differential Equations, CRC Press, Boca Raton–London, 2023.
3. A. D. Polyanin and A. I. Zhurov, Separation of Variables and Exact Solutions to Nonlinear PDEs, CRC Press, Boca Raton–London, 2021.
4. A. D. Polyanin and V. F. Zaitsev, Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, CRC Press, Boca Raton–London, 2018.
5. A. D. Polyanin and V. E. Nazaikinskii, Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition (Updated, Revised and Extended), CRC Press, Boca Raton–London, 2016.
6. A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, 2nd Edition (Updated, Revised and Extended), Chapman & Hall/CRC Press, Boca Raton–London, 2012.
7. A. D. Polyanin and A. I. Chernoutsan (Eds.), A Concise Handbook of Mathematics, Physics, and Engineering Sciences, Chapman & Hall/CRC Press, Boca Raton–London, 2010.
8. A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, 2nd Edition (Updated, Revised and Extended), Chapman & Hall/CRC Press, Boca Raton–London, 2008.
9. A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton–London, 2007.
10. A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton–London, 2004.
11. A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition (Updated and Extended), CRC Press, Boca Raton–New York, 2003.
12. A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton–London, 2002.
13. A. D. Polyanin, V. F. Zaitsev, and A. Moussiaux, Handbook of First Order Partial Differential Equations, Taylor & Francis, London, 2002.
14. A. D. Polyanin, A. M. Kutepov, et al., Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Taylor & Francis, London, 2002.
15. A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton–Boston–London, 1998.
16. A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, Boca Raton–New York, 1995.
17. V. F. Zaitsev and A. D. Polyanin, Discrete-Group Methods for Integrating Equations of Nonlinear Mechanics, CRC Press/Begell House, Boca Raton–Ann Arbor, 1994.
18. A. D. Polyanin and V. V. Dilman, Methods of Modeling Equations and Analogies in Chemical Engineering, CRC Press/Begell House, Boca Raton–Ann Arbor, 1994.

Books in German

1. A. D. Polyanin, A.V. Manzhirov, Handbuch der Integralgleichungen: Exakte Loesungen, Spektrum Akademischer Verlag, Heidelberg–Berlin, 1999.
2. A. D. Polyanin, V. F. Zaitsev, Handbuch der linearen Differentialgleichungen, Spektrum Akademischer Verlag, Heidelberg–Berlin, 1996.
3. A.D. Poljanin, V.F. Sajzew, Sammlung gewöhnlicher Differentialgleichungen, Verlag Harri Deutsch, Frankfurt am Main, 1996.

Books in Russian: click here

Selected Articles Since 2012

• Polyanin, A. D. and Zhurov, A. I., On RF-pairs, Bäcklund transformations and linearization of nonlinear equations, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 2, pp. 536–544, 2012. (See a preprint of the article in ResearchGate)
• Polyanin, A. D. and Zhurov, A. I., On order reduction of non-linear equations of mechanics and mathematical physics, new integrable equations and exact solutions, International Journal of Non-Linear Mechanics, Vol. 47, No. 5, pp. 413–417, 2012. (See a preprint of the article in ResearchGate)
• Polyanin, A. D. and Zhurov, A. I., Integration of linear and some model non-linear equations of motion of incompressible fluids, International Journal of Non-Linear Mechanics, Vol. 49, pp. 77–83, 2013. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Exact solutions of linear and non-linear differential-difference heat and diffusion equations with finite relaxation time, International Journal of Non-Linear Mechanics, Vol. 54, pp. 115–126, 2013. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Exact solutions of non-linear differential-difference equations of a viscous fluid with finite relaxation time, International Journal of Non-Linear Mechanics, Vol. 57, p. 116–122, 2013. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Exact separable solutions of delay reaction-diffusion equations and other nonlinear partial functional-differential equations, Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 3, pp. 409–416, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations, Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 3, pp. 417–430, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. New generalized and functional separable solutions to non-linear delay reaction-diffusion equations, International Journal of Non-Linear Mechanics, Vol. 59, p. 16–22, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Generalized and functional separable solutions to nonlinear delay Klein–Gordon equations, Communications in Nonlinear Science and Numerical Simulation , Vol. 19, No. 8, pp. 2676–2689, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Non-linear instability and exact solutions to some delay reaction-diffusion systems, International Journal of Non-Linear Mechanics, Vol. 62, pp. 33–40, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Nonlinear delay reaction-diffusion equations with varying transfer coefficients: Exact methods and new solutions, Applied Mathematics Letters, Vol. 37, pp. 43–48, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. The functional constraints method: Application to non-linear delay reaction-diffusion equations with varying transfer coefficients, International Journal of Non-Linear Mechanics, Vol. 67, pp. 267–277, 2014. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. The generating equations method: Constructing exact solutions to delay reaction-diffusion systems and other non-linear coupled delay PDEs, International Journal of Non-Linear Mechanics, Vol. 71, pp. 104–115, 2015. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, V. G. Sorokin. Nonlinear delay reaction-diffusion equations: Traveling-wave solutions in elementary functions, Applied Mathematics Letters, Vol. 46, pp. 38–43, 2015. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Unsteady axisymmetric boundary-layer equations: Transformations, properties, exact solutions, order reduction and solution method, International Journal of Non-Linear Mechanics, Vol. 74, pp. 40–50, 2015. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations, Communications in Nonlinear Science and Numerical Simulation, Vol. 31, No. 1-3, pp. 11–20, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Functional and generalized separable solutions to unsteady Navier-Stokes equations, International Journal of Non-Linear Mechanics, Vol. 79, pp. 88–98, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, S. A. Lychev. Decomposition methods for coupled 3D equations of applied mathematics and continuum mechanics: Partial survey, classification, new results, and generalizations, Applied Mathematical Modelling, Vol. 40, No. 4, pp. 3298–3324, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Parametrically defined nonlinear differential equations and their solutions: Applications in fluid dynamics, Applied Mathematics Letters, Vol. 55, pp. 72–80, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Non-isothermal flows of liquid metals and melts: Qualitative features, asymptotic models, problems, exact and approximate solutions, International Journal of Non-Linear Mechanics, Vol. 82, pp. 104–113, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. One-dimensional reductions and functional separable solutions to unsteady plane and axisymmetric boundary-layer equations for non-Newtonian fluids, International Journal of Non-Linear Mechanics, Vol. 85, pp. 70–80, 2016. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, A. I. Zhurov. Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: Transformations, general solutions, and integration methods, Applied Mathematics Letters, Vol. 64, pp. 59–66, 2017. (See a preprint of the article)
• A. D. Polyanin, I. K. Shingareva. The use of differential and non-local transformations for numerical integration of non-linear blow-up problems, International Journal of Non-Linear Mechanics, Vol. 95, pp. 178–184, 2017. (See a preprint of the article)
• A. D. Polyanin, I. K. Shingareva. Non-monotonic blow-up problems: Test problems with solutions in elementary functions, numerical integration based on non-local transformations, Applied Mathematics Letters, Vol. 76, pp. 123–129, 2018. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, I. K. Shingareva. Hypersingular nonlinear boundary-value problems with a small parameter, Applied Mathematics Letters, Vol. 81, pp. 93–98, 2018. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, I. K. Shingareva. Non-linear problems with non-monotonic blow-up solutions: Non-local transformations, test problems, exact solutions, and numerical integration, International Journal of Non-Linear Mechanics, Vol. 99, pp. 258–272, 2018. (See a preprint of the article in ResearchGate)
• A. D. Polyanin, I. K. Shingareva. Application of non-local transformations for numerical integration of singularly perturbed boundary-value problems with a small parameter, International Journal of Non-Linear Mechanics, Vol. 103, pp. 37–54, 2018. (See a preprint of the article)
• A. D. Polyanin, I. K. Shingareva. Overdetermined systems of ODEs with parameters and their applications: The method of differential constraints and the generalized separation of variables in PDEs, Mathematical Advances in Pure and Applied Sciences, Vol. 1, No. 1, pp. 1–22, 2018. (See the article in ResearchGate)
• A. D. Polyanin, I. K. Shingareva. Nonlinear problems with blow-up solutions: Numerical integration based on differential and nonlocal transformations, and differential constraints, Applied Mathematics and Computation, Vol. 336, pp. 107–137, 2018. (See a preprint of the article)
• A. D. Polyanin. Functional separable solutions of nonlinear reaction-diffusion equations with variable coefficients, Applied Mathematics and Computation, Vol. 347, pp. 282–292, 2019. (See a preprint of the article)
• A. D. Polyanin. Generalized traveling-wave solutions of nonlinear reaction-diffusion equations with delay and variable coefficients, Applied Mathematics Letters, Vol. 90, pp. 49–53, 2019. (See a preprint of the article)
• A. D. Polyanin. Functional separable solutions of nonlinear convection-diffusion equations with variable coefficients, Communications in Nonlinear Science and Numerical Simulation, Vol. 73, pp. 379–390, 2019. (See a preprint of the article)
• A. D. Polyanin, I. K. Shingareva. Non-linear blow-up problems for systems of ODEs and PDEs: Non-local transformations, numerical and exact solutions, International Journal of Non-Linear Mechanics, Vol. 111, pp. 28–41, 2019.
• A. D. Polyanin. Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction-diffusion equations with variable coefficients, International Journal of Non-Linear Mechanics, Vol. 111, pp. 95–105, 2019. (See a preprint of the article)
• A. D. Polyanin. Comparison of the effectiveness of different methods for constructing exact solutions to nonlinear PDEs. Generalizations and new solutions, Mathematics, Vol. 7, No. 5, 386, 2019; doi:10.3390/math7050386 (See the article)
• A. D. Polyanin. Construction of functional separable solutions in implicit form for non-linear Klein--Gordon type equations with variable coefficients, International Journal of Non-Linear Mechanics, Vol. 114, pp. 29–40, 2019. (See a preprint of the article)
• A. D. Polyanin. Functional separation of variables in nonlinear PDEs: General approach, new solutions of diffusion-type equations, Mathematics, 2020, Vol. 8, No. 1, 90; doi:10.3390/math8010090 (See the article)
• A. D. Polyanin, A. I. Zhurov. Separation of variables in PDEs using nonlinear transformations: Applications to reaction-diffusion type equations, Applied Mathematics Letters, 2020, Vol. 100, 106055. (See a preprint of the article)
• A. I. Zhurov, A. D. Polyanin. Symmetry reductions and new functional separable solutions of nonlinear Klein–Gordon and telegraph type equations, Journal of Nonlinear Mathematical Physics, 2020, Vol. 27, No. 2, pp. 227–242.
• A. D. Polyanin, V. G. Sorokin. New exact solutions of nonlinear wave type PDEs with delay, Applied Mathematics Letters, 2020, Vol. 108, 106512.
• A. D. Polyanin, V. G. Sorokin. A method for constructing exact solutions of nonlinear delay PDEs, Journal of Mathematical Analysis and Applications, 2021, Vol. 494, 124619.
• A. D. Polyanin, V. G. Sorokin. Construction of exact solutions to nonlinear PDEs with delay using solutions of simpler PDEs without delay, Communications in Nonlinear Science and Numerical Simulation, 2021, Vol. 95, 105634.
• A. V. Aksenov, A. D. Polyanin. Methods for constructing complex solutions of nonlinear PDEs using simpler solutions, Mathematics, 2021, Vol. 9, No. 4, 345; doi:10.3390/math9040345 (See the article)
• A. D. Polyanin, V. G. Sorokin, Nonlinear pantograph-type diffusion PDEs: Exact solutions and the principle of analogy, Mathematics, 2021, Vol. 9, No. 5, 511; doi:10.3390/math9050511 (See the article)
• A. D. Polyanin, I. K. Shingareva, The similarity index of scientific publications with equations and formulas, identification of self-plagiarism, and testing of the iThenticate system, Mathematical Modeling and Computational Methods, 2021, No. 2, pp. 96–116 (See the article)
• A. D. Polyanin, A. I. Zhurov. Multi-parameter reaction-diffusion systems with quadratic nonlinearity and delays: New exact solutions in elementary functions, Mathematics, 2022, Vol. 10, No. 9, 1529; doi:10.3390/math10091529 (See the article)
• A. D. Polyanin, V. G. Sorokin, Reductions and exact solutions of nonlinear wave-type PDEs with proportional and more complex delays, Mathematics, 2023, Vol. 11, No. 3, 516; doi:10.3390/math11030516 (See the article)
• A. D. Polyanin, V. G. Sorokin, Exact solutions of reaction-diffusion PDEs with anisotropic time delay, Mathematics, 2023, Vol. 11, No. 14, 3111; doi:10.3390/math11143111 (See the article)
• A. D. Polyanin, A. V. Aksenov, Unsteady magnetohydrodynamics PDE of Monge-Ampère type: Symmetries, closed-form solutions, and reductions, Mathematics, 2024, Vol. 12, No. 13, 2127; doi:10.3390/math12132127 (See the article)
• A. D. Polyanin, Principle of structural analogy of solutions and its application to nonlinear PDEs and delay PDEs, Journal of Mathematical Sciences, 2024; doi:10.1007/s10958-024-07234-6 (See the article)
• A. D. Polyanin, N. A. Kudryashov, Nonlinear Schrödinger equations with delay: Closed-form and generalized separable solutions, Contemporary Mathematics, 2024; doi:10.1007/s10958-024-07234-6 (See the article)
• A. D. Polyanin, N. A. Kudryashov, Closed-form solutions of the nonlinear Schrödinger equation with arbitrary dispersion and potential, Chaos, Solitons & Fractals, 2025, Vol. 191, 115822; doi:10.1016/j.chaos.2024.115822 (See the article)

External Links:

• Biographical information, Wikipedia, the free encyclopedia
• List of publications, Google Scholar
• List of publications, ResearchGate

Photographs:

• Andrei Polyanin with his books, 2004 - 1
• Andrei Polyanin with his books, 2004 - 2

E-mail: polyanin@ipmnet.ru
Home page: http://eqworld.ipmnet.ru/polyanin-ew.htm

Mailing Address:
Institute for Problems in Mechanics
Russian Academy of Sciences
101 Vernadsky Avenue, Bldg 1
119526 Moscow, Russia

Page last updated: December 8, 2024

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