Group analysis, differential equations,mathematical physics, mathematical modelling, Riemannian geometry.
Main publications:
N.Kh. Ibragimov, “Konformanaya invariantnost i printsip Gyuigensa”, Doklady Akademii nauk SSSR, 194:1 (1970), 24-27
N.Kh. Ibragimov, “Invariantnye variatsionnye zadachi i zakony sokhraneniya (zamechaniya k teoreme Neter)”, Teoreticheskaya i matematicheskaya fizika, 1:3 (1969), 350-359
N.Kh. Ibragimov, “K teorii grupp preobrazovanii Li-Beklunda”, Matematicheskii sbornik, 109 (151):2 (1979), 229-253
N.Kh. Ibragimov, Gruppy preobrazovanii v matematicheskoi fizike, Nauka, Moskva, 1983
N.H. Ibragimov, A practical course in differential equations and mathematical modelling., Russkii per.: Prakticheskii differentsialnykh uravnenii i matematicheskogo modelirovaniya. Fizmatlit. 2012, Higher Education Press and World Scientific, Beijing, Singapore, 2009
R. K. Gazizov, N. H. Ibragimov, “Approximate symmetries and solutions of the Kompaneets equation”, Prikl. Mekh. Tekh. Fiz., 55:2 (2014), 38–42; J. Appl. Mech. Tech. Phys., 55:2 (2014), 220–224
N. Kh. Ibragimov, E. D. Avdonina, “Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws”, Uspekhi Mat. Nauk, 68:5(413) (2013), 111–146; Russian Math. Surveys, 68:5 (2013), 889–921
N. H. Ibragimov, C. Rogers, “On infinitesimal reciprocal-type transformations in gasdynamics. Lie group connections and nonlinear self-adjointness”, Ufimsk. Mat. Zh., 4:4 (2012), 196–207
A. A. Alexandrova, N. H. Ibragimov, K. V. Imamutdinova, V. O. Lukashchuk, “Local and nonlocal conserved vectors for the nonlinear filtration equation”, Ufimsk. Mat. Zh., 4:4 (2012), 179–185
E. D. Avdonina, N. H. Ibragimov, “Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation”, Ufimsk. Mat. Zh., 4:1 (2012), 6–16
N. H. Ibragimov, “Invariants of hyperbolic equations: solution of the Laplace problem”, Prikl. Mekh. Tekh. Fiz., 45:2 (2004), 11–21; J. Appl. Mech. Tech. Phys., 45:2 (2004), 158–166
V. A. Baikov, R. K. Gazizov, N. H. Ibragimov, “Approximate equivalence transformations”, Differ. Uravn., 30:10 (1994), 1659–1664; Differ. Equ., 30:10 (1994), 1531–1535
1993
8.
N. H. Ibragimov, “Seven notes on group analysis”, Differ. Uravn., 29:10 (1993), 1739–1750; Differ. Equ., 29:10 (1993), 1511–1520
9.
V. A. Baikov, R. K. Gazizov, N. H. Ibragimov, “Approximate groups of transformations”, Differ. Uravn., 29:10 (1993), 1712–1732; Differ. Equ., 29:10 (1993), 1487–1504
N. Kh. Ibragimov, “Group analysis of ordinary differential equations and the invariance principle in mathematical physics (for the 150th anniversary of Sophus Lie)”, Uspekhi Mat. Nauk, 47:4(286) (1992), 83–144; Russian Math. Surveys, 47:4 (1992), 89–156
N. Kh. Ibragimov, A. O. Oganesyan, “The hierarchy of Huygens equations in spaces with a non-trivial conformal group”, Uspekhi Mat. Nauk, 46:3(279) (1991), 111–146; Russian Math. Surveys, 46:3 (1991), 137–176
V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov, “Approximate symmetries and preservation laws”, Trudy Mat. Inst. Steklov., 200 (1991), 35–45; Proc. Steklov Inst. Math., 200 (1993), 35–47
V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov, “Perturbation methods in group analysis”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 34 (1989), 85–147; J. Soviet Math., 55:1 (1991), 1450–1490
I. Sh. Akhatov, R. K. Gazizov, N. Kh. Ibragimov, “Nonlocal symmetries. Heuristic approach”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 34 (1989), 3–83; J. Soviet Math., 55:1 (1991), 1401–1450
A. V. Bobylev, N. Kh. Ibragimov, “Intenconnectivity of symmetry properties for equations of dynamics, kinetic theory of gases, and hydrodynamics”, Mat. Model., 1:3 (1989), 100–109
V. A. Baikov, R. K. Gazizov, N. H. Ibragimov, “Approximate symmetry and formal linearization”, Prikl. Mekh. Tekh. Fiz., 30:2 (1989), 40–49; J. Appl. Mech. Tech. Phys., 30:2 (1989), 204–212
V. A. Baikov, R. K. Gazizov, N. H. Ibragimov, “Linearization and formal symmetries of the Korteweg-de Vries
equation”, Dokl. Akad. Nauk SSSR, 303:4 (1988), 781–784; Dokl. Math., 38:3 (1989), 588–591
18.
V. A. Baikov, R. K. Gazizov, N. H. Ibragimov, “Approximate group analysis of the nonlinear equation $u_{tt}-(f(u)u_x)_x+\varepsilon\varphi(u)u_t=0$”, Differ. Uravn., 24:7 (1988), 1127–1138; Differ. Equ., 24:7 (1988), 719–728
19.
V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov, “Approximate symmetries”, Mat. Sb. (N.S.), 136(178):4(8) (1988), 435–450; Math. USSR-Sb., 64:2 (1989), 427–441
I. Sh. Akhatov, R. K. Gazizov, N. H. Ibragimov, “Bäcklund transforms and nonlocal symmetries”, Dokl. Akad. Nauk SSSR, 297:1 (1987), 11–14
21.
I. Sh. Akhatov, R. K. Gazizov, N. H. Ibragimov, “Quasilocal symmetries of equations of nonlinear heat-conduction
type”, Dokl. Akad. Nauk SSSR, 295:1 (1987), 75–78
I. Sh. Akhatov, R. K. Gazizov, N. H. Ibragimov, “Group classification of equations of nonlinear filtration”, Dokl. Akad. Nauk SSSR, 293:5 (1987), 1033–1035
N. Kh. Ibragimov, A. B. Shabat, “Evolutionary equations with nontrivial Lie–Bäcklund group”, Funktsional. Anal. i Prilozhen., 14:1 (1980), 25–36; Funct. Anal. Appl., 14:1 (1980), 19–28
N. Kh. Ibragimov, “On the theory of Lie–Bäcklund transformation groups”, Mat. Sb. (N.S.), 109(151):2(6) (1979), 229–253; Math. USSR-Sb., 37:2 (1980), 205–226
N. Kh. Ibragimov, E. V. Mamontov, “On the Сauchy problem for the equation $u_{tt}-u_{xx}-\sum_{i,j=1}^{n-1}a_{ij}(x-t)u_{y_iy_j}=0$”, Mat. Sb. (N.S.), 102(144):3 (1977), 391–409; Math. USSR-Sb., 31:3 (1977), 347–363
N. H. Ibragimov, “Classification of the invariant solutions to the equations for the two-dimensional transient-state flow of a gas”, Prikl. Mekh. Tekh. Fiz., 7:4 (1966), 19–22; J. Appl. Mech. Tech. Phys., 7:4 (1966), 11–13