METHODS FOR SEPARATION OF VARIABLES AND EXACT SOLUTIONS NONLINE-AR EQUATIONS OF MATHEMATICAL PHYSICS
https://doi.org/10.26583/vestnik.2023.260
Abstract
Methods of generalized and functional separation of variables used to find exact solutions to nonlinear equations of mathematical physics are considered. A direct method for constructing reductions (in many ways similar to methods of functional separation of variables) and its more general version based on the principle of splitting are described. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology and other physics, heat and mass transfer equations, hydrodynamic equations are studied.
About the Author
A. V. Aksenov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Faculty of Mechanics and Mathematics
References
1. Polyanin A.D., Zhurov A.I. Metody razdeleniya peremennyh i tochnye resheniya nelinejnyh uravnenij matematicheskoj fiziki. [Methods for separating varia-bles and exact solutions of nonlinear equations of mathematical physics]. Moscow. Institute of Mechanics and Mechanics RAS Publ., 2020.
2. Polyanin A.D. 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, 2019, Vol. 111, pp. 95–105.
3. Polyanin A.D. Construction of functional separa-ble solutions in implicit form for non-linear Klein--Gordon type equations with variable coefficients. Inter-national Journal of Non-Linear Mechanics, 2019, Vol. 114, pp. 29–40.
4. Polyanin A.D. Functional separation of variables in nonlinear PDEs: General approach, new solutions of diffusion-type equations. Mathematics, 2020, Vol. 8, No. 1, 90.
5. Polyanin A.D., Zhurov A.I. Separation of variables in PDEs using nonlinear transformations: Applications to reaction-diffusion type equations. Applied Mathematics Letters, 2020, Vol. 100, 106055.
Review
For citations:
Aksenov A.V. METHODS FOR SEPARATION OF VARIABLES AND EXACT SOLUTIONS NONLINE-AR EQUATIONS OF MATHEMATICAL PHYSICS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(2):131-132. (In Russ.) https://doi.org/10.26583/vestnik.2023.260
Views:
172
Email this article 