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@article{SJIM_2022_25_1_a0, author = {Yu. E. Anikonov and M. V. Neshchadim and A. P. Chupakhin}, title = {Multidimensional {Hopf} equation and some exact solutions}, journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki}, pages = {5--13}, publisher = {mathdoc}, volume = {25}, number = {1}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a0/} }
TY - JOUR AU - Yu. E. Anikonov AU - M. V. Neshchadim AU - A. P. Chupakhin TI - Multidimensional Hopf equation and some exact solutions JO - Sibirskij žurnal industrialʹnoj matematiki PY - 2022 SP - 5 EP - 13 VL - 25 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a0/ LA - ru ID - SJIM_2022_25_1_a0 ER -
%0 Journal Article %A Yu. E. Anikonov %A M. V. Neshchadim %A A. P. Chupakhin %T Multidimensional Hopf equation and some exact solutions %J Sibirskij žurnal industrialʹnoj matematiki %D 2022 %P 5-13 %V 25 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a0/ %G ru %F SJIM_2022_25_1_a0
Yu. E. Anikonov; M. V. Neshchadim; A. P. Chupakhin. Multidimensional Hopf equation and some exact solutions. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 1, pp. 5-13. http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a0/
[1] L. V. Ovsyannikov, Group Analysis of Differential Equations, Acad. Press, N.Y., 1982 | MR | MR | Zbl
[2] A. P. Chupakhin, Barochronous gas motions: general properties and submodels of types (1, 2) and (1, 1), Preprint, No 4-98, Lavrentyev Institute of Hydrodynamics SO RAN, Novosibirsk, 1998
[3] M. I. Zelikin, Homogeneous spaces and the Riccati equation in the calculus of variations, Faktorial, M., 1998 (in Russian)
[4] F. A. Chernous'ko, V. B. Kolmanovskii, Optimal control under random perturbations, Nauka, M., 1978 (in Russian)
[5] L. V. Ovsyannikov, Lectures on the Fundamentals of Gas Dynamics, Institute of Computer Science, M.–Izhevsk, 2003 (in Russian) | MR
[6] A. P. Chupakhin, Nonbarochronous Submodels of Types (1, 2) and (1, 1) of the Gas Dynamics Equations, Preprint No 1-99, Lavrentyev Institute of Hydrodynamics SO RAN, Novosibirsk, 1999
[7] A. A. Cherevko, A. P. Chupakhin, The Stationary Ovsyannikov Vortex, Preprint, No 1-2005, Lavrentyev Institute of Hydrodynamics SO RAN, Novosibirsk, 2005 | MR
[8] Miller E., “A regularity criterion for the Navier-Stokes equation involving only the middle eigenvalue of the strain tensor”, Arch. Rational Mech. Anal., 235 (2020), 99–139 | DOI | MR | Zbl
[9] S. C. Anco, G. M. Webb, “Hierarchies of new invariants and conserved integrals in inviscid fluid flow”, Phys. Fluids, 32 (2020), 086104 | DOI
[10] A. L. Karchevsky, “The direct dynamical problem of seismics for horizontally stratified media”, Siberian Electronic Math. Reports, 2 (2005), 23–61 | Zbl
[11] A. L. Karchevsky, “A frequency-domain analytical solution of Maxwell-s equations for layered anisotropic media”, Russian Geology and Geophysics, 48:8 (2007), 689–695 | DOI
[12] A. L. Karchevsky, “Analytical solutions of the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for the boundary conditions of various types”, J. Appl. Indust. Math., 14:4 (2020), 648–665 | DOI | MR
[13] M. V. Neshchadim, A. P. Chupakhin, “On integration of a matrix Riccati equation”, J. Appl. Indust. Math., 14:4 (2020), 732–742 | DOI | MR
[14] M. V. Neshchadim, A. P. Chupakhin, “Method of commutators for integration of a matrix Riccati equation”, J. Appl. Indust. Math., 15:1 (2021), 78–86 | DOI | MR
[15] J. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Mid-Country Press, London, 1978 | MR | MR
[16] A. F. Sidorov, V. P. Shapeev, N. N. Yanenko, Method of differential constraints and applications in gas dynamics, Nauka, Novosibirsk, 1984 (in Russian) | MR
[17] S. P. Finikov, Cartan's Method of Exterior Forms, Gostekhizdat, M., 1948 (in Russian)
[18] M. A. Evgrafov, Analitical functions, Lan, St. Petersburg, 2008 (in Russian)
[19] S. Lang, Algebra, Graduate Texts in Mathematics, Springer, 2002 | MR | Zbl
[20] A. M. Grundland, “Invariant solutions of hydrodynamic-type equations”, J. Phys. Math. Gen., 33 (2000), 8193–8215 | DOI | MR | Zbl
[21] P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, N.Y., 1986 | MR | Zbl