01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
3.01.1955
E-mail:
Keywords:
dynamical systems,
higher symmetries,
inverse scattering transform method,
characteristic algebras
initial boundary value problem,
Korteweg–de Vries type equations.
Subject:
Integrable nonlinear equations of mathematical physics.
Biography
Graduated from Faculty of Mathematics of the Bashkirian State University in 1977 (department of differential equations). Ph.D. thesis (supervisor A.B.Shabat) was defended in 1982. D.Sci. thesis was defended in 1996. Since 1993 he has been working at the Institute of Mathematics of the Ufa Federal Research Center of the Russian Academy of Sciences, at the present time - Head of the Department of Mathematical Physics.
Main publications:
I. T. Habibullin, “Symmetries of boundary problems”, Phys. Let. A, 178 (1993), 369–375
I. T. Khabibullin, “O zadache lineinogo sopryazheniya na okruzhnosti”, Matematicheskie zametki, 41:3 (1987), 342–347
I. T. Khabibullin, “Nachalno-kraevaya zadacha dlya uravneniya KdF na poluosi s odnorodnymi kraevymi usloviyami”, TMF, 130:1 (2002), 31–53
I. T. Habibullin, T. G. Kazakova, “Boundary conditions for integrable discrete chains”, J. Phys. A: Math. Gen., 34 (2001), 10369–10376
I. T. Khabibullin, “Nachalno-kraevaya zadacha na poluosi dlya uravneniya MKdF”, Funkts. analiz i ego prilozh., 34:1 (2000), 65–75
I. T. Habibullin, A. R. Khakimova, A. O. Smirnov, “Construction of exact solutions to the Ruijsenaars-Toda lattice via generalized invariant manifolds”, Nonlinearity, 36:1 (2023), 231-254
M. N. Kuznetsova, I. T. Habibullin, A. R. Khakimova, “On the problem of classifying integrable chains with three independent variables”, Theoret. and Math. Phys., 215:2 (2023), 667–690
3.
I. T. Habibullin, A. R. Khakimova, “On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras”, Theoret. and Math. Phys., 217:1 (2023), 1541–1573
4.
I. T. Habibullin, A. R. Khakimova, A. U. Sakieva, “Miura-Type Transformations for Integrable Lattices in 3D”, Mathematics, 11:16 (2023), 3522 , 15 pp.
K. I. Faizulina, I. T. Habibullin, A. R. Khakimova, “Laplace transformations and sine-Gordon type integrable PDE”, Journal of Physics A: Mathematical and Theoretical, 57:1 (2023), 015203 , 21 pp.
6.
I. T. Habibullin, A. R. Khakimova, “Integrals and characteristic algebras for systems of discrete equations on a quadrilateral graph”, Theoret. and Math. Phys., 213:2 (2022), 1589–1612
7.
I. T. Habibullin, A. R. Khakimova, “Algebraic reductions of discrete equations of Hirota-Miwa type”, Ufa Math. J., 14:4 (2022), 113–126
8.
I. T. Habibullin, A. R. Khakimova, “Characteristic Lie algebras of integrable differential-difference equations in 3D”, Journal of Physics A: Mathematical and Theoretical, 54:29 (2021), 295202 , 34 pp.
R. N. Garifullin, I. T. Habibullin, “Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations”, Journal of Physics A: Mathematical and Theoretical, 54:20 (2021), 205201 , 19 pp.
I. T. Habibullin, A. R. Khakimova, “Invariant manifolds of hyperbolic integrable equations and their applications”, Journal of Mathematical Sciences, 257:3 (2021), 410–423
I. T. Habibullin, M. N. Kuznetsova, “An algebraic criterion of the Darboux integrability of differential-difference equations and systems”, Journal of Physics A: Mathematical and Theoretical, 54 (2021), 505201 , 20 pp.
I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices
via Lie–Rinehart algebras”, Theoret. and Math. Phys., 203:1 (2020), 569–581
14.
I. T. Habibullin, A. R. Khakimova, “Integrable Boundary Conditions for the Hirota-Miwa Equation and Lie Algebras”, Journal of Nonlinear Mathematical Physics, 27:3 (2020), 393–413
I. T. Habibullin, A. R. Khakimova, “Invariant manifolds and separation of the variables for integrable chains”, Journal of Physics A: Mathematical and Theoretical, 53:38 (2020), 385202 , 17 pp.
E. V. Ferapontov, I. T. Habibullin, M. N. Kuznetsova, V. S. Novikov, “On a class of 2D integrable lattice equations”, Journal of Mathematical Physics, 61:7 (2020), 073505 , 15 pp.
I. T. Habibullin, M. N. Kuznetsova, A. U. Sakieva,, “Integrability conditions for two-dimensional Toda-like equations”, Journal of Physics A: Mathematical and Theoretical, 53:39 (2020), 395203 , 25 pp.
I. T. Habibullin, A. R. Khakimova, “Invariant manifolds of hyperbolic integrable equations and their applications”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 136–150
19.
I. T. Habibullin, A. R. Khakimova, “Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A^{(1)}_{N-1}$”, Journal of Physics A: Mathematical and Theoretical, 52:36 (2019), 365202 , 29 pp.
I. T. Khabibullin, A. R. Khakimova, “Algoritm postroeniya pary Laksa i operatora rekursii dlya integriruemykh uravnenii”, Okeanologicheskie issledovaniya, 47:1 (2019), 123–126
21.
E. V. Pavlova, I. T. Habibullin, A. R. Khakimova, “On One Integrable Discrete System”, Journal of Mathematical Sciences, 241:4 (2019), 409–422
I. T. Khabibullin, M. N. Poptsova, “Integrable two-dimensional lattices. Characteristic Lie rings and classification.”, Journal of Mathematical Sciences, 241:4 (2019), 396–4008
23.
I. T. Habibullin, A. R. Khakimova, “A direct algorithm for constructing recursion operators and Lax pairs for integrable models”, Theoret. and Math. Phys., 196:2 (2018), 1200–1216
24.
I. T. Habibullin, A. R. Khakimova,, “On the recursion operators for integrable equations”, Journal of Physics A: Mathematical and Theoretical, 51:42 (2018), https://doi.org/10.1088/1751-8121/aade08 , 22 pp.
M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105
26.
I. T. Habibullin, A. R. Khakimova, “Invariant manifolds and Lax pairs for integrable nonlinear chains”, Theoret. and Math. Phys., 191:3 (2017), 793–810
27.
E. V. Pavlova, I. T. Habibullin, A. R. Khakimova, “On one integrable discrete system”, Journal of Mathematical Sciences, 241:4 (2019), 409–422
28.
I. T. Habibullin, M. N. Poptsova, “Integrable two-dimensional lattices. Characteristic Lie rings and classification”, Journal of Mathematical Sciences, 241:4 (2019), 396–408
29.
Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 73 , 26 pp.
A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, Uravneniya matematicheskoi fiziki. Nelineinye integriruemye uravneniya, Seriya : Universitety Rossii, 2-e izd., ispr. i dop., M.: Izdatelstvo Yurait, 111123, g. Moskva, ul. Plekhanova, d.4a., 2017 , 375 pp., Uchebnoe posobie dlya bakalavriata i magistratury
31.
I. T. Habibullin, A. R. Khakimova, “On a method for constructing the Lax pairs for integrable models via a quadratic ansatz”, Journal of Physics A: Mathematical and Theoretical, 50 (2017), 305206 , 19 pp., arXiv: 1702.04533
I. T. Khabibullin, M. N. Poptsova, “Integriruemye dvumerizovannye tsepochki. Kharakteristicheskie koltsa Li i klassifikatsiya.”, Ufimskaya matematicheskaya konferentsiya s mezhdunarodnym uchastiem, Sbornik tezisov (g. Ufa, 27–30 sentyabrya 2016 goda.), RITs BashGU., g. Ufa, 2016, 173–174
33.
M. N. Poptsova, I. T. Habibullin, “Symmetries and conservation laws for a two-component discrete potentiated Korteweg–de Vries equation”, Ufa Math. Journal, 8:3 (2016), 109–121
34.
I. T. Khabibullin, A. R. Khakimova, “Ob odnom metode postroeniya par Laksa dlya integriruemykh sistem”, Ufimskaya matematicheskaya konferentsiya s mezhdunarodnym uchastiem, sbornik tezisov (g. Ufa, 27–30 sentyabrya 2016 g.), RITs BashGU., g. Ufa, 2016, 175
35.
I. Habibullin, N. Zheltukhina, “Discretization of Liouville type nonautonomous equations preserving integrals”, Journal of Nonlinear Mathematical Physics, 23:4 (2016), 620–642 , Taylor & Francis
I. T. Habibullin, A. R. Khakimova, M. N. Poptsova, “On a method for constructing the Lax pairs for nonlinear integrable equations”, Journal of Physics A: Mathematical and Theoretical, 49 (2016), 035202 , 35 pp., arXiv: 1506.02563
I. T. Habibullin, M. N. Poptsova, “Asymptotic diagonalization of the discrete Lax pair around singularities and conservation laws for dynamical systems”, Journal of Physics A: Mathematical and Theoretical, 48:11 (2015), 115203 , IOP Publishing
R. N. Garifullin, I. T. Habibullin, R. I. Yamilov, “Peculiar symmetry structure of some known discrete nonautonomous equations”, Journal of Physics A: Mathematical and Theoretical, 48:23 (2015), 235201 , IOP Publishing
I. T. Habibullin, M. V. Yangubaeva, “Formal diagonalization of a discrete Lax operator and conservation laws and symmetries of dynamical systems”, Theoret. and Math. Phys., 177:3 (2013), 1655–1679
40.
I. Habibullin, “Characteristic Lie rings, finitely-generated modules and integrability conditions for (2+ 1)-dimensional lattices”, Physica Scripta, 87:6 (2013), 065005 , IOP Publishing
A. V. Zhiber, R. D. Murtazina, I. T. Habibullin, A. B. Shabat, “Characteristic Lie rings and integrable models in mathematical physics”, Ufimsk. Mat. Zh., 4:3 (2012), 17–85
43.
M. Gürses, A. V. Zhiber, I. T. Habibullin, “Characteristic Lie rings of differential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 53–62
44.
R. N. Garifullin, I. T. Habibullin, “Affine Lie algebras, Lax pairs and integrable discrete and continuous systems”, 2012, arXiv: 1205.6620
45.
A. V. Zhiber, R. D. Murtazina, I. T. Habibullin, A. B. Shabat, “Characteristic Lie rings and integrable models in mathematical physics”, Moscow-Izhevsk: Institute of Computer Science, 2012
46.
A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, “Kharakteristicheskie koltsa Li i integriruemye modeli matematicheskoi fiziki”, Ufimsk. matem. zhurn., 4:3 (2012), 17–85
I. Habibullin, K. Zheltukhin, M. Yangubaeva, “Cartan matrices and integrable lattice Toda field equations”, Journal of Physics A: Mathematical and Theoretical, 44:46 (2011), 465202 , IOP Publishing
I. Habibullin, N. Zheltukhina, A. Sakieva, “Discretization of hyperbolic type Darboux integrable equations preserving integrability”, Journal of Mathematical Physics, 52:9 (2011), 093507
R. N. Garifullin, E. V. Gudkova, I. T. Habibullin, “Method for searching higher symmetries for quad-graph equations”, Journal of Physics A: Mathematical and Theoretical, 44:32 (2011), 325202 , IOP Publishing
N. A. Zheltukhina, A. U. Sakieva, I. T. Habibullin, “Characteristic Lie algebra and Darboux integrable discrete chains”, Ufimsk. Mat. Zh., 2:4 (2010), 39–51
53.
I. Habibullin, N. Zheltukhina, A. Sakieva, “On Darboux-integrable semi-discrete chains”, Journal of Physics A: Mathematical and Theoretical, 43:43 (2010), 434017 , IOP Publishing
M. A. Shamsutdinov, I. T. Khabibullin, A. T. Kharisov, A. P. Tankeyev, “Dynamics of magnetic kinks in exchange-coupled ferromagnetic layers”, The Physics of Metals and Metallography, 108:4 (2009), 327–340 , Sp Maik Nauka/Interperiodica
I. Habibullin, N. Zheltukhina, A. Pekcan, “Complete list of Darboux integrable chains of the form t1x=tx+d„t , t1…”, Journal of Mathematical Physics, 50:102710 (2009), 1–23 , American Institute of Physics
56.
I. Habibullin, A. Kundu, “Quantum and classical integrable sine-Gordon model with defect”, Nuclear Physics B, 795:3 (2008), 549–568 , Elsevier
M. Gürses, I. Habibullin, K. Zheltukhin, “Hydrodynamic type integrable equations on a segment and a half-line”, Journal of Mathematical Physics, 49:10 (2008), 102704 , AIP Publishing
58.
I. Habibullin, N. Zheltukhina, A. Pekcan, “On the classification of Darboux integrable chains”, Journal of Mathematical Physics, 49:102702 (2008), 1–39 , AIP
59.
I. Habibullin, A. Pekcan, N. Zheltukhina, “On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations”, Turkish J. Math., 32:3 (2008), 277–292 , Tubitak
60.
I. T. Habibullin, A. Pekcan, “Characteristic Lie algebra and classification of semidiscrete models”, Theoret. and Math. Phys., 151:3 (2007), 781–790
61.
M. Gurses, I. Habibullin, K. Zheltukhin, “Integrable boundary value problems for elliptic type Toda lattice in a disk”, Journal of Mathematical Physics, 48:10 (2007), 102702 , American Institute of Physics
I. T. Habibullin, “Truncations of Toda chains and the reduction problem”, Theoret. and Math. Phys., 143:1 (2005), 515–528
66.
I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funct. Anal. Appl., 38:2 (2004), 138–148
67.
E. V. Gudkova, I. T. Habibullin, “Kadomtsev–Petviashvili Equation on the Half-Plane”, Theoret. and Math. Phys., 140:2 (2004), 1086–1094
68.
I. T. Habibullin, “Multidimensional integrable boundary problems”, arXiv preprint nlin/0401028, 2004
69.
I. T. Habibullin, “Integrable initial boundary value problems”, Matem. fiz., anal., geom., 9:2 (2002), 261–267
70.
I. T. Habibullin, “Initial Boundary Value Problem for the KdV Equation on a Semiaxis with Homogeneous Boundary Conditions”, Theoret. and Math. Phys., 130:1 (2002), 25–44
71.
I. T. Habibullin, T. G. Kazakova, “Boundary conditions for integrable discrete chains”, Journal of Physics A: Mathematical and General, 34:48 (2001), 10369 , IOP Publishing
I. T. Habibullin, A. N. Vil’danov, “Boundary conditions consistent with LA pairs”, Proc. Intl. Conf. Mogran 2000, 2000, 80–82
75.
I. T. Habibullin, “KdV equation on a half-line with the zero boundary condition”, Theoret. and Math. Phys., 119:3 (1999), 712–718
76.
I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, Theoret. and Math. Phys., 114:1 (1998), 90–98
77.
I. Habibullin, “Integrable boundary conditions for nonlinear partial differential equations”, Exactly Solvable Models in Mathematical Physics, 1998
78.
V. E. Adler, I. T. Habibullin, “Boundary Conditions for Integrable Lattices”, Funct. Anal. Appl., 31:2 (1997), 75–85
79.
V. E. Adler, I. T. Habibullin, A. B. Shabat, “Boundary value problem for the KdV equation on a half-line”, Theoret. and Math. Phys., 110:1 (1997), 78–90
80.
V. Adler, B. Gürel, M. Gürses, I. Habibullin, “Boundary conditions for integrable equations”, Journal of Physics A: Mathematical and General, 30:10 (1997), 3505 , IOP Publishing
B. Gürel, I. Habibullin, “Boundary conditions for two-dimensional integrable chains”, Physics Letters A, 233:1 (1997), 68–72 , North-Holland
82.
S. I. Svinolupov, I. T. Habibullin, “Integrable boundary conditions for many-component burgers equations”, Math. Notes, 60:6 (1996), 671–680
83.
I. T. Habibullin, VV. Sokolov, R. I. Yamilov, “Multi-component integrable systems and nonassociative structures”, Nonlinear Physics: theory and experiment World Scientific Publishing, 1996 , Dtic Document
84.
I. T. Habibullin, “Symmetry approach in boundary value problems”, Journal of Nonlinear Mathematical Physics, 3:1-2 (1996), 147–151 , Taylor & Francis Group
T. B. Gürel, M. Gürses, I. Habibullin, “Integrable boundary conditions for evolution equations”, Proc. Workshop on Nonlinear Physics: Theory and Experiment (Lecce, 1995), 1996
86.
B. Gürel, M. Gürses, I. Habibullin, “Boundary value problems for integrable equations compatible with the symmetry algebra”, Journal of Mathematical Physics, 36:12 (1995), 6809–6821 , AIP Publishing
V. E. Adler, I. T. Habibullin, “Integrable boundary conditions for the Toda lattice”, Journal of Physics A: Mathematical and General, 28:23 (1995), 6717 , IOP Publishing
I. T. Habibullin, S. I. Svinolupov, “Integrable boundary value problems for the multicomponent Schrödinger equations”, Physica D: Nonlinear Phenomena, 87:1 (1995), 134–139 , North-Holland
B. Gürel, M. Gürses, I. Habibullin, “Boundary value problems compatible with symmetries”, Physics Letters A, 190:3 (1994), 231–237 , North-Holland
91.
B. I. Suleimanov, I. T. Habibullin, “Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes”, Theoret. and Math. Phys., 97:2 (1993), 1250–1258
92.
I. T. Habibullin, “Boundary conditions for nonlinear equations compatible with integrability”, Theoret. and Math. Phys., 96:1 (1993), 845–853
93.
I. T. Habibullin, “Symmetries of boundary problems”, Physics Letters A, 178:5 (1993), 369–375 , Elsevier
I. T. Habibullin, “Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method”, Theoret. and Math. Phys., 91:3 (1992), 581–590
95.
I. T. Habibullin, “The Bäcklund transformation and integrable initial boundary value problems”, Math. Notes, 49:4 (1991), 18–23
96.
I. T. Habibullin, “Integrable initial-boundary-value problems”, Theoret. and Math. Phys., 86:1 (1991), 28–36
97.
I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, Theoret. and Math. Phys., 83:3 (1990), 565–573
98.
I. T. Habibullin, “Backlund transformation and integrable boundary-initial value problems”, Nonlinear world: IV International Workshop on Nonlinear and Turbulent Processes in Physics, 1, 1990, 130
99.
I. T. Habibullin, A. G. Shagalov, “Numerical solution of the Riemann problem of analytic conjugation”, U.S.S.R. Comput. Math. Math. Phys., 29:2 (1989), 39–45
100.
I. T. Habibullin, “Problem of linear conjugation on a circumference”, Math. Notes, 41:3 (1987), 195–198
101.
I. T. Habibullin, “Discrete Zakharov–Shabat systems and integrable equations”, Differential geometry, Lie groups and mechanics. Part VII, Zap. Nauchn. Sem. LOMI, 146, “Nauka”, Leningrad. Otdel., Leningrad, 1985, 137–146
102.
V. Yu. Novokshenov, I. T. Habibullin, Sov. Math. Doklady, 23, no. 2, 1981, 304–307
103.
V. Yu. Novokshenov, I. T. Habibullin, “Nonlinear differential-difference schemes integrable by the method of the inverse scattering problem. Asymptotics of the solution for $t\to\infty$”, Dokl. Akad. Nauk SSSR, 257:3 (1981), 543–547
104.
I. T. Habibullin, “The Inverse Scattering Problem For Difference Equations”, Soviet Math. Dokl., 20:6 (1979), 1233–1236 , Mezhdunarodnaya Kniga
105.
I. T. Khabibullin, “Obratnaya zadacha rasseyaniya dlya raznostnykh uravnenii”, Doklady AN SSSR, M., 1079, t.249, # 1, s.67-70., 249:1 (1979), 67-70
106.
I. T. Habibullin, “The inverse scattering problem for difference equations”, Dokl. Akad. Nauk SSSR, 249:1 (1979), 67–70
107.
V. E. Adler, P. Winternitz, R. N. Garifullin, A. V. Zhiber, D. Levi, A. V. Mikhailov, I. Kh. Musin, F. W. Nijhoff, V. V. Sokolov, B. I. Suleimanov, E. V. Ferapontov, A. P. Fordy, I. T. Habibullin, I. Yu. Cherdantsev, R. A. Sharipov, R. S. Yulmukhametov, “In memory of Yamilov Ravil Islamovich”, Ufa Math. J., 12:3 (2020), 119–120
108.
L. A. Kalyakin, V. Yu. Novokshenov, I. T. Habibullin, E. G. Ekomasov, A. T. Kharisov, “In memory of Miniakhat Asgatovich Shamsutdinov”, Ufimsk. Mat. Zh., 3:1 (2011), 122–123