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. U. Sakieva, “On integrable reductions reductions of two-dimensional Toda-type lattices”, Partial Differential Equations In Applied Mathematics, 11 (2024), 100854 , 9 pp.
2.
I. T. Habibullin, A. R. Khakimova, “Construction of exact solutions of nonlinear PDE via dressing chain in 3D”, Ufa Mathematical Journal, 16:4 (2024), 124–135
2023
3.
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
5.
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
6.
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.
2022
8.
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
9.
I. T. Habibullin, A. R. Khakimova, “Algebraic reductions of discrete equations of Hirota-Miwa type”, Ufa Math. J., 14:4 (2022), 113–126
2021
10.
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
16.
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.
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
2019
21.
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
22.
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
24.
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
2018
26.
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
27.
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
2017
29.
I. T. Habibullin, A. R. Khakimova, “Invariant manifolds and Lax pairs for integrable nonlinear chains”, Theoret. and Math. Phys., 191:3 (2017), 793–810
2019
30.
E. V. Pavlova, I. T. Habibullin, A. R. Khakimova, “On one integrable discrete system”, Journal of Mathematical Sciences, 241:4 (2019), 409–422
31.
I. T. Habibullin, M. N. Poptsova, “Integrable two-dimensional lattices. Characteristic Lie rings and classification”, Journal of Mathematical Sciences, 241:4 (2019), 396–408
2017
32.
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
34.
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
36.
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
37.
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
38.
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
43.
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
46.
M. Gürses, A. V. Zhiber, I. T. Habibullin, “Characteristic Lie rings of differential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 53–62
47.
R. N. Garifullin, I. T. Habibullin, “Affine Lie algebras, Lax pairs and integrable discrete and continuous systems”, 2012, arXiv: 1205.6620
48.
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
49.
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
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
2010
56.
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
57.
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
2008
60.
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
62.
I. Habibullin, N. Zheltukhina, A. Pekcan, “On the classification of Darboux integrable chains”, Journal of Mathematical Physics, 49:102702 (2008), 1–39 , AIP
63.
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
2007
64.
I. T. Habibullin, A. Pekcan, “Characteristic Lie algebra and classification of semidiscrete models”, Theoret. and Math. Phys., 151:3 (2007), 781–790
65.
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
2004
70.
I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funct. Anal. Appl., 38:2 (2004), 138–148
71.
E. V. Gudkova, I. T. Habibullin, “Kadomtsev–Petviashvili Equation on the Half-Plane”, Theoret. and Math. Phys., 140:2 (2004), 1086–1094
72.
I. T. Habibullin, “Multidimensional integrable boundary problems”, arXiv preprint nlin/0401028, 2004
2002
73.
I. T. Habibullin, “Integrable initial boundary value problems”, Matem. fiz., anal., geom., 9:2 (2002), 261–267
74.
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
2001
75.
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
1999
79.
I. T. Habibullin, “KdV equation on a half-line with the zero boundary condition”, Theoret. and Math. Phys., 119:3 (1999), 712–718
1998
80.
I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, Theoret. and Math. Phys., 114:1 (1998), 90–98
81.
I. Habibullin, “Integrable boundary conditions for nonlinear partial differential equations”, Exactly Solvable Models in Mathematical Physics, 1998
1997
82.
V. E. Adler, I. T. Habibullin, “Boundary Conditions for Integrable Lattices”, Funct. Anal. Appl., 31:2 (1997), 75–85
83.
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
84.
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
1996
86.
S. I. Svinolupov, I. T. Habibullin, “Integrable boundary conditions for many-component burgers equations”, Math. Notes, 60:6 (1996), 671–680
87.
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
88.
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
1995
90.
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
1993
95.
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
96.
I. T. Habibullin, “Boundary conditions for nonlinear equations compatible with integrability”, Theoret. and Math. Phys., 96:1 (1993), 845–853
97.
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
1991
99.
I. T. Habibullin, “The Bäcklund transformation and integrable initial boundary value problems”, Math. Notes, 49:4 (1991), 18–23
100.
I. T. Habibullin, “Integrable initial-boundary-value problems”, Theoret. and Math. Phys., 86:1 (1991), 28–36
1990
101.
I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, Theoret. and Math. Phys., 83:3 (1990), 565–573
102.
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
1989
103.
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
1987
104.
I. T. Habibullin, “Problem of linear conjugation on a circumference”, Math. Notes, 41:3 (1987), 195–198
1985
105.
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
1981
106.
V. Yu. Novokshenov, I. T. Habibullin, Sov. Math. Doklady, 23, no. 2, 1981, 304–307
107.
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
1979
108.
I. T. Habibullin, “The Inverse Scattering Problem For Difference Equations”, Soviet Math. Dokl., 20:6 (1979), 1233–1236 , Mezhdunarodnaya Kniga
109.
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
110.
I. T. Habibullin, “The inverse scattering problem for difference equations”, Dokl. Akad. Nauk SSSR, 249:1 (1979), 67–70