Надіслати цю статтю Про симетрійну редукцію (1+3)-вимірного неоднорідного рівняння Монжа–Ампера до алгебраїчних рівнянь
Анотація
Зразок для цитування: В. М. Федорчук, В. І. Федорчук, “Про симетрійну редукцію (1+3)-вимірного неоднорідного рівняння Монжа–Ампера до алгебраїчних рівнянь,” Мат. методи та фіз.-мех. поля, 65, No. 1-2, 58–64 (2022), https://doi.org/10.15407/mmpmf2022.65.1-2.58-64
Ключові слова
Посилання
L. V. Ovsiannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978); [in English]: Acad. Press, New York (1982).
A. V. Pogorelov, The Minkowski Multidimensional Problem [in Russian], Nauka, Moscow (1975).
V. M. Fedorchuk, V. I. Fedorchuk, “On classification of the low-dimensional non-conjugated subalgebras of the Lie algebra of the Poincare group P(1,4),” in: Symmetry and Integrability of the Equations of Mathematical Physics, Collection of Works of Institute of Mathematics, NAS of Ukraine, 3, No. 2, 301–307 (2006) (in Ukrainian).
V. M. Fedorchuk, V. I. Fedorchuk, “Reduction of the (1+3)-dimensional inhomogeneous Monge–Ampère equation to first-order partial differential equations,” Ukr. Mat. Zh., 74, No. 3, 418–426 (2022), https://doi.org/10.37863/umzh.v74i3.6996; English translation: Ukr. Math. J., 74, No. 3, 472–483 (2022), https://doi.org/10.1007/s11253-022-02076-4
W. I. Fushchich, A. G. Nikitin, Symmetry of Equations of Quantum Mechanics [in Russian], Nauka, Moscow (1990); [in English] Allerton Press, New York (1994).
W. I. Fushchich, N. I. Serov, “Symmetry and some exact solutions of the multidimensional Monge–Ampère equation,” Dokl. Akad. Nauk SSSR, 273, No. 3, 543–546 (1983) (in Russian).
S. V. Khabirov, “Application of contact transformations of the inhomogeneous Monge–Ampère equation in one-dimensional gas dynamics,” Dokl. Akad. Nauk SSSR, 310, No. 2, 333–336 (1990); English translation: Sov. Phys. Dokl., 35, No. 1., 29–30 (1990).
M. J. P. Cullen, R. J. Douglas, “Applications of the Monge–Ampère equation and Monge transport problem to meteorology and oceanography,” in: L. A. Caffarelli, M. Milman (eds), Monge–Ampère Equation: Applications to Geometry and Optimization, Vol. 226 of Contemp. Math., Amer. Math. Soc., Providence, RI (1999), pp. 33–53, https://doi.org/10.1090/conm/226/03234
V. Fedorchuk,” Symmetry reduction and exact solutions of the Euler–Lagrange–Born–Infeld, multidimensional Monge–Ampère and eikonal equations,” J. Nonlinear Math. Phys., 2, No. 3-4, 329–333 (2013), https://doi.org/10.2991/jnmp.1995.2.3-4.13.
V. Fedorchuk, V. Fedorchuk, Classification of Symmetry Reductions for the Eikonal Equation, IAPMM, NAS of Ukraine, Lviv (2018).
V. Fedorchuk, V. Fedorchuk, “On classification of symmetry reductions for partial differential equations,” in: Non-classical Problems of Theory of Differential Equations, Collection of scientific works dedicated to 80th anniversary of B. Yo. Ptashnyk, IAPMM, NAS of Ukraine, Lviv (2017), pp. 241–255.
V. M. Fedorchuk, V. I. Fedorchuk, “On symmetry reduction of the (1+3)-dimensional inhomogeneous Monge–Ampère equation to the first-order ODEs,” Appl. Math., 11, No. 11, 1178–1195 (2020), https://doi.org/10.4236/am.2020.1111080
A. M. Grundland, J. Harnad, P. Winternitz, “Symmetry reduction for nonlinear relativistically invariant equations,” J. Math. Phys., 25, No. 4, 791–806 (1984), https://doi.org/10.1063/1.526224
C. E. Gutierrez, T. van Nguyen, “On Monge–Ampère type equations arising in optimal transportation problems,” Calcul. Var. Partial Differ. Equat., 28, No. 3, 275–316 (2007), https://doi.org/10.1007/s00526-006-0045-x
F. Jiang, N. S. Trudinger, “On the second boundary value problem for Monge–Ampère type equations and geometric optics,” Arch. Ration. Mech. Anal., 229, No. 2, 547–567 (2018), https://doi.org/10.1007/s00205-018-1222-8
A. Kushner, V. V. Lychagin, J. Slovák , “Lectures on geometry of Monge–Ampère equations with Maple,” in: R. A. Kycia, M. Ulan, E. Schneider (Eds.), Nonlinear PDEs, their Geometry, and Applications, Birkhäuser, Basel (2019), Chapt. 2, pp. 53–94, https://doi.org/10.1007/978-3-030-17031-8_2
S. Lie, Zur allgemeinen Theorie der partiellen Differentialgleichungen beliebiger Ordnung, Berichte, Leipzig (1895), S. 53–128.
A. G. Nikitin, O. Kuriksha, “Invariant solutions for equations of axion electrodynamics,” Commun. Nonlinear Sci. Numer. Simulat., 17, No. 12, 4585–4601 (2012), https://doi.org/10.1016/j.cnsns.2012.04.009
P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York (1986), https://doi.org/10.1007/978-1-4684-0274-2
Ł. T. Stępień, “On some exact solutions of heavenly equations in four dimensions,” AIP Advances, 10, Art. 065105 (2020), https://doi.org/10.1063/1.5144327
C. Udrişte, N. Bilă, “Symmetry group of Ţiţeica surfaces PDE,” Balkan J. Geom. Appl., 4, No. 2, 123–140 (1999).
E. Witten, “Superstring perturbation theory via super Riemann surfaces: an overview,” Pure Appl. Math. Quart., 15, No. 1, 517–607 (2019), https://doi.org/10.4310/PAMQ.2019.v15.n1.a4
Yau Shing-Tung, Nadis Steve, The Shape of a Life. One Mathematician’s Search for the Universe’s Hidden Geometry, Yale Univ. Press, New Haven (2019).
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