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1.В.А.Дородницын, Ю.П.Попов. О стационарных режимах
излучающего сильноточного самосжатого разряда в плазме. ЖВМ и МФ, 13, N 1 (1973), 247-253.
2.В.А.Дородницын, С.П.Курдюмов, Ю.П.Попов, А.А.Самарский. Образование Т-слоев при торможении плазмы магнитным полем. ДАН СССР, 216 (1974), N 6, 1254-1257.
3.В.А.Дородницын. Об инвариантных решениях уравнения нелинейной теплопроводности с источником. ЖВМ МФ, 22 (1982), 1393-1400.
4.V.A.Dorodnitsyn, G.G.Elenin, S.P.Kurdyumov. Exact invariant solutions of some problems for quasi linear parabolic equations. Banakh international mathematical center, Warsaw, Poland, v. 13 (1983), 113-123.
5.В.А.Дородницын, C.Р.Свирщевский, И.В.Князева. Групповые свойства уравнения теплопроводности с источником в двумерном и трехмерном случаях. Диф. Уравнения, 19 (1983), 1215-1223.
6.V.A.Galaktionov, V.A.Dorodnitsyn, G.G.Elenin, S.P.Kurdyumov, A.A. Samarskii. A Quasi linear Heat Transfer Equation with a Source: Blow up, Localization, Symmetry, Exact Solutions, Asymptotics, Structures. Journal of Soviet Mathematics, v.41, N 5, p. 1222-1292, 1988, New York.
7. М.И.Бакирова, С.Н.Димова, В.А.Дородницын, С.П.Курдюмов, А.А.Самарский, С.Р.Свирщевский. Инвариантные решения уравнения теплопроводности, описывающие направленное распространение горения и спиральные волны в нелинейной среде. ДАН СССР, 299 (1988), 346-351. (Translation in Soviet Phys. Dokl. 33 (1988), no 3, 187-189.)
8.V.A.Dorodnitsyn, G.G.Elenin. Symmetry of the nonlinear phenomena, Computers and nonlinear phenomena. Modern Natural Science. - Moscow: Nauka, 1988, 123-191, (Russian).
9.V.A.Dorodnitsyn, S.R.Svirshchevskii. The symmetry of the system of equations of nonlinear optical phase conjugation. Preprint Inst. Appl. Mathem. Acad. Sci. USSR, N 114, 1990, (Russian); see also CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 2, Applications in Engineering and Physical Sciences, CRC Press, 1995, p. 450-452.
10.V.A.Dorodnitsyn. Transformation groups in a space of difference variables. Journal of Soviet Mathematics, 1991 (June), v.55, N 1, Plenum Publishing Corporation, p.1490-1517.
11. В.А.Дородницын. Конечно-разностный аналог теоремы Нетер, ДАН, 1993, v. 328, N6, p.678-682.
12.V.Dorodnitsyn, Invariant discrete model for the Korteweg-de-Vries equation, Preprint of CRM, Centre de Resherches Mathematiques, Universite de Montreal, CRM - 2187, May 1994.
13.V.A.Dorodnitsyn. Finite-difference models entirely inheriting symmetry of original differential equations. Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, p. 191-201, Kluwer Academic Publisher, 1993.
14.M.I.Bakirova, V.A.Dorodnitsyn. Invariant finite-difference model for semilinear heat transfer equation, Journ. Differencialnyie Uravnenia, v.30, N 10, pp. 1697-1702, 1994 (Russian).
15.V.A.Dorodnitsyn. Finite-difference models entirely inheriting continuous symmetry of original differential equations, International Journal of Modern Physics C, (Physics and Computers), vol.5, N4, 1994, p.723-734.
16.V.Dorodnitsyn, Some new invariant difference equations on evolutionary grids, Proceedings of 14-th IMACS World Congress of Computational and Applied Mathematics, V.1, p.143-146, 1994.
17.V.Dorodnitsyn, Continuous symmetries of finite-difference evolution equations and grids,
Proceedings of Workshop on Symmetries and Integrability of Difference Equations, CRM, University of Montreal, Vol. 9, p.103-112, 1996.
18.V.Dorodnitsyn, Group theoretical methods for finite difference modeling, Proceedings of the First World Congress of Nonlinear Analysts, Walter de Gruyter, p.979-990, 1996.
19.M.Bakirova, V.Dorodnitsyn, R.Kozlov, Invariant difference schemes for heat transfer equations with a source, J. Phys. A: Math.Gen., 30, 8139-8155, 1997.
20.V.Dorodnitsyn, Noether-type theorems for difference equations, Applied Numerical Mathematics, v. 39, No 3-4, 307-321, 2001; See also: V.Dorodnitsyn, Noether-type theorems for difference equations, Preprint of the Institut des Hautes Etudes Scientifiques, IHES/M/98/27, Bures-sur-Yvette, France, 1998.
21.V.Dorodnitsyn, Conservation Laws for Difference Equations, in Modern Group Analysis VII, Developments in Theory, Computation and Application, ed. by N.H.Ibragimov, K.Razi Naqvi, E.Straume, MARS Publishers, Symmetry Foundation, 91-97, 1999.
22.V.Dorodnitsyn, P.Winternitz, Lie point symmetry preserving discretizations for variable coefficient Korteweg - de -Vries equations, Nonlinear Dynamics, v. 22, No 1, 49-59, Kluwer Academic Publishers, 2000.
23.V.Dorodnitsyn, R.Kozlov, P.Winternitz, Lie group classification of second-order ordinary difference equations, J.Math.Phys., v.41, No 1, 480-504, 2000.
24.V.Dorodnitsyn, Invariant difference model for nonlinear Schroedinger equation with conservation of Lagrangian structure, Proceedings of the International conference MOGRAN 2000, ed. by N.H.Ibragimov , 49-52, Ufa, 2001.
25.C.Budd, V.Dorodnitsyn, Symmetry-adapted moving mesh schemes for the nonlinear
Schroedinger equation, J. Phys. A: Math.Gen., v.34, N 48, 10387-10400, 2001.
26.V.Dorodnitsyn, R.Kozlov, A heat transfer with a source: the complete set of invariant difference schemes, J. of Nonlinear Math. Physics, v. 10, N 1, 16-50, 2003.
27.V.Dorodnitsyn, R.Kozlov, P.Winternitz, Symmetries, Lagrangian formalism and integration of second order ODEs, J. of Nonlinear Math. Phys, v.10, N2, 41-56, 2003.
28.V.Dorodnitsyn,R.Kozlov, P.Winternitz, Continuous symmetries of Lagrangians and exact solutions of discrete equations, J. of Math. Physics, 45, No1, 336-359, 2004.
29.V.Dorodnitsyn, Lie group properties of difference equations, MAKS-Press, Moscow, 210 p., 2000. The new edition: Moscow, “Nauka”, 236 p., 2001.
30.V.Dorodnitsyn, On the linearization of second-order differential and difference equations, Sigma, Vol.2 (2006), paper 065, nlin SI/0608038.
31.V.Dorodnitsyn, Non-autonomous dynamical systems and exact solutions with superposition principle for evolution PDEs ,(Russian) 2009.
32. A.Bobylev, V.Dorodnitsyn, Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation, DCDS-A, Vol.24, N1, 35-57, 2009.
33. V.Dorodnitsyn, On the exact difference schemes for second-order difference equations with symmetries, Special issue: Lectures of Applied Mathematics, 327-342, URSS, Moscow, 2009, (Russian).
34. V.Dorodnitsyn, R.Kozlov, Invariance and first integrals of continuous and discrete Hamiltonian equations, Journal of Engineering Mathematics, 2009.
35. V.Dorodnitsyn, R.Kozlov, Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals, SMS Lecture Notes, Cambridge University Press, 2011.
36. V.Dorodnitsyn, Applications of Lie Groups to Difference Equations, Chapman and Hall/CRC, 264 p., 2011.
37. V.A. Dorodnitsyn, E. I. Kaptsov, R. V. Kozlov, and P. Winternitz. The adjoint equation method for constructing first integrals of difference equations. Journal of Physics A: Mathematical and Theoretical, 48(5):055202, 01 2015.
38. Dorodnitsyn V.A., Kozlov R., Meleshko S.V., One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes. Communications in Nonlinear Science and Numerical Simulation. v.74, 2019.
39.V. A. Dorodnitsyn and E. I. Kaptsov. Shallow water equations in Lagrangian coordinates: Symmetries, conservation laws and its preservation in difference models. Commun. Nonlinear. Sci. Numer. Simulat., 89:105343, 2020.
40. A. F. Cheviakov, V. A. Dorodnitsyn, and E. I. Kaptsov. Invariant conservation lawpreserving discretizations of linear and nonlinear wave equations. Journal of Mathematical Physics, 61(8):081504, 2020.
41. V. A. Dorodnitsyn, E. I. Kaptsov, and S. V. Meleshko. Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations. Journal of Nonlinear Mathematical Physics, 28:90–107, 2020.
42. Dorodnitsyn V.A. , Kaptsov E.I., Shallow water equations in Lagrangian coordinates:Symmetries, conservation laws and its preservation in difference models Communications in Nonlinear Science and Numerical Simulation {89} (2020)
43. V.A. Dorodnitsyn and E. I. Kaptsov. Discrete shallow water equations preserving symmetries and conservation laws. Journal of Mathematical Physics, 62(8):083508, 2021.
44. V.A. Dorodnitsyn, E.I. Kaptsov and S.V. Meleshko, Symmetries, Conservation Laws, Invariant Solutions and Difference Schemes of the One-dimensional Green-Naghdi Equations Journal of Nonlinear Mathematical Physics, 2021.
45. V. A. Dorodnitsyn, E. I. Kaptsov, R. V. Kozlov, and S. V Meleshko. One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws. International Journal of Non-Linear Mechanics, 2022.
46. V.Dorodnitsyn, R.Kozlov, S. Meleshko, Lagrangian formalism and Noether-type theorems for second-order delay ordinary differential equations, Journal of Physics A: Mathematical and Theoretical, JPhysA-118973.R1, 2023
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