Construction of exact solutions to nonlinear equations of the hyperbolic type
DOI:
https://doi.org/10.15407/dopovidi2017.07.003Keywords:
differential equations, generalized separation of variables, nonlinear hyperbolic equationsAbstract
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Galaktionov, V. A. & Posashkov, S. A. (1994). Tochnye resheniia i invariantnye prostranstva dlia nelineinykh uravnenii gradientnoi diffuzii. Zhurn. vychisl. matem. i matem. fiziki, 34, No. 3, pp. 373-383 (in Russian).
Galaktionov, V. A. (1995). Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities. Proc. Math. Roy. Soc. Edinb. 125, Iss. 2, pp. 225-246. https://doi.org/10.1017/S0308210500028018
Galaktionov, V. A., Posashkov, S. A. & Svirshchevskii, S. R. (1995). Generalized separation of variables for differential equations with polynomial nonlinearities. Differents. uravneniya, 31, No. 2, pp. 253-261 (in Russian); Differ. Equat., 31, Iss. 2, pp. 233-240.
Galaktionov, V. A. & Svirshchevskii, S. R. (2007). Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics. Boca Raton, London: Chapman & Hall/CRC.
Barannyk, A., Barannyk, T. & Yuryk, I. (2011). Separation of variables for nonlinear equations of hyperbolic and Korteweg–de Vries type. Rep. Math. Phys., 68, Iss. 1, pp. 97-105. https://doi.org/10.1016/S0034-4877(11)60029-3
Barannyk, A.F., Barannyk, T.A., & Yuryk, I.I. (2013). Generalized Separation of Variables for Nonlinear Equation utt = F(u)uxx + aF′(u)ux2 . Rep. Math. Phys., 71, Iss. 1, pp. 1-13. https://doi.org/10.1016/S0034-4877(13)60018-X
Polyanin, A. D. & Zaitsev, V. F. (2004). Handbook of nonlinear partial differential equations. Boca Raton, London: Chapman & Hall/CRC.
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