Email this article On one method for constructing exact solutions of nonlinear equations of mathematical physics
- Authors: Polyanin A.D.1,2, Zhurov A.I.1
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
- Issue: Vol 489, No 3 (2019)
- Pages: 235-239
- Section: Mathematical physics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18578
- DOI: https://doi.org/10.31857/S0869-56524893235-239
- ID: 18578
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Abstract
A new method for constructing exact solutions of nonlinear equations of mathematical physics, which is based on nonlinear integral type transformations in combination with the splitting principle, is proposed. The effectiveness of the method is illustrated on nonlinear equations of the reaction-diffusion type, which depend on two or three arbitrary functions. New exact functional separable solutions and generalized traveling wave solutions are described.
About the authors
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Author for correspondence.
Email: polyanin@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526; 31, Kashirskoe shosse, Moscow, 115409
A. I. Zhurov
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Email: zhurov@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526
References
- Полянин А.Д., Зайцев В.Ф., Журов А.И. Методы решения нелинейных уравнений математической физики и механики. М.: Физматлит, 2005.
- Galaktionov V.A., Svirshchevskii S.R. Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics. Boca Raton: Chapman & Hall/CRC Press, 2007.
- Polyanin A.D., Zaitsev V.F. Handbook of Nonlinear Partial Differential Equations. 2nd Ed. Boca Raton: CRC Press, 2012.
- Grundland A.M., Infeld E. // J. Math. Phys. 1992. V. 33. P. 2498-2503.
- Zhdanov R.Z. // J. Phys. A. 1994. V. 27. P. L291-L297.
- Галактионов В.А., Посашков С.А., Свирщевский С.Р. // Дифференц. уравнения. 1995. Т. 31. № 2. C. 253-261.
- Doyle Ph.W., Vassiliou P.J. // Int. J. Non-Linear Mech. 1998. V. 33. № 2. P. 315-326.
- Polyanin A.D., Zhurov A.I. // Int. J. Non-Linear Mech. 2016. V. 79. P. 88-98.
- Polyanin A.D. // Applied Math. Comput. 2019. V. 347. P. 282-292.
- Polyanin A.D. // Commun. Nonlinear Sci. Numer. Simulat. 2019. V. 73. P. 379-390.
- Polyanin A.D. // Int. J. Non-Linear Mech. 2019. V. 111. P. 95-105; V. 114. P. 29-40.
- Овсянников Л.В. Групповой анализ дифференциальных уравнений. М.: Наука, 1978.
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