Scientific interests: Painleve ordinary differential equations, their higher analogues and applications, behaviour of solutions of PDE with small parameter near typical singularities of limiting equations. It is shown that universal special functions of wave catastrophes - solutions of nonlinear integrable PDE - are solutions of higher analogues of Painleve ODE.
Biography
Graduated from Bashikirian state unversity in 1980 (department of of differential equations). Ph.D. thesis was defended in 2010. A list of my works contains 37 titles.
Main publications:
Suleimanov B. I., Khabibullin I. T. Simmetrii uravneniya Kadomtseva–Petviashvili, izomonodromnye deformatsii i "nelineinye" obobscheniya nelineinykh spetsialnykh funktsii volnovykh katastrof // Teoreticheskaya i matematicheskaya fizika, 1993, 97, 2, 213–226.
Suleimanov B. I. Vozniknovenie bezdissipativnykh udarnykh voln i "neperturbativnaya" kvantovaya teoriya gravitatsii // Zhurnal eksperimentalnoi i teoreticheskoi fiziki, 1994, 105, 5, 1089–1097.
Suleimanov B. I. Gamiltonova struktura uravnenii Penleve i metod izomonodromnykh deformatsii // Differentsialnye uravneniya, 1994, 30, 5, 791–795.
Kudashev V. R., Suleimanov B. I. Osobennosti nekotorykh tipichnykh protsessov samoproizvolnogo padeniya intensivnosti v neustoichivykh sredakh // Pisma v zhurnal eksperimentalnoi i teoreticheskoi fiziki, 1995, 62, 4, 358–363.
Kudashev V. R., Suleimanov B. I. Vliyanie maloi dissipatsii na protsessy zarozhdeniya odnomernykh udarnykh voln // Prikladnaya matematika i mekhanika. 2001, 65, 3, 456–466.
B. I. Suleimanov, “Zeros of solutions of third-order L–A pairs and linearizable ordinary differential equations”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S230–S238
2022
2.
B. I. Suleimanov, A. M. Shavlukov, “Inheritance of Generic Singularities of Solutions of a Linear Wave Equation by Solutions of Isoentropic Gas Motion Equations”, Math. Notes, 112:4 (2022), 608–620
3.
A. V. Domrin, M. A. Shumkin, B. I. Suleimanov, “Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type”, Journal of Mathematical Physics, 63:2 (2022), 023501 (2022) (Published online) , 18 pp. https://aip.scitation.org/doi/10.1063/5.0075416, arXiv: https://arxiv.org/abs/2110.09858
B. I. Suleimanov, A. M. Shavlukov, “Integrable Abel equation and asymptotics
of symmetry solutions of Korteweg-de Vries equation”, Ufa Math. J., 13:2 (2021), 99–106
2022
5.
B. I. Suleimanov, “Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom”, St. Petersburg Math. J., 33:6 (2022), 995–1009
2020
6.
A. V. Domrin, B. I. Suleimanov, M. A. Shumkin, “Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies”, Proc. Steklov Inst. Math., 311 (2020), 98–113
7.
B. I. Suleimanov, A. M. Shavlukov, “Tipichnaya provalnaya osobennost sborki reshenii uravnenii dvizheniya
odnomernogo izoentropicheskogo gaza”, Izvestiya RAN. Seriya fizicheskaya., T. 84:# 5 (2020), S. 664–666.
8.
V. A. Pavlenko, B. I. Suleimanov, “Yavnye resheniya analogov vremennykh uravnenii Shredingera s gamiltonovoi sistemoi $H^{4+1}$.”, Izvestiya RAN. Seriya fizicheskaya., T. 84:# 5 (2020), S. 695–698
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
10.
B. I. Suleimanov, “On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 81–95
2018
11.
V. A. Pavlenko, B. I. Suleimanov, “Solutions to analogues of non-stationary Schrödinger equations defined by isomonodromic Hamilton system $H^{2+1+1+1}$”, Ufa Math. J., 10:4 (2018), 92–102
2017
12.
A. A. Ershov, B. I. Suleimanov, “Some Features of Bending of a Rod
under a Strong Longitudinal Compression”, Russian Journal of Mathematical Physics, 24:2 (2017), 216–233
B. I. Suleimanov, “Effect of a small dispersion on self-focusing in a spatially one-dimensional case”, JETP Letters, 106:6 (2017), 400–405
14.
V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$”, Ufa Math. Journal, 9:4 (2017), 97–107
2016
15.
D. P. Novikov, B. I. Suleimanov, ““Quantization” of an isomonodromic Hamiltonian Garnier system with two degrees of freedom”, Theoret. and Math. Phys., 187:1 (2016), 479–496
16.
B. I. Suleimanov, “Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential”, Ufa Math. Journal, 8:3 (2016), 136–154
2014
17.
B. I. Suleimanov, ““Quantizations” of Higher Hamiltonian Analogues of the Painlevé I and Painlevé II Equations with Two Degrees of Freedom”, Funct. Anal. Appl., 48:3 (2014), 198–207
2013
18.
B. I. Suleimanov, “Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 137–145
2012
19.
B. I. Suleimanov, “The “quantum” linearization of the Painlevé equations as a component of theier $L,A$ pairs”, Ufimsk. Mat. Zh., 4:2 (2012), 127–135
20.
B. I. Suleimanov, “Generic singularities in solutions of the shallow water equations”, Doklady Mathematics, 85, no. 1, 2012, 125–128
R. Garifullin, B. Suleimanov, N. Tarkhanov, “Phase shift in the Whitham zone for the Gurevich–Pitaevskii special solution of the Korteweg–de Vries equation”, Physics Letters A, 374:13 (2010), 1420–1424
R. N. Garifullin, B. I. Suleimanov, “From weak discontinuities to nondissipative shock waves”, Journal of Experimental and Theoretical Physics, 110:1 (2010), 133–146
B. I. Suleimanov, “On the Solution of Boundary-Value Problems of Kolmogorov–Petrovskii–Piskunov Type”, Math. Notes, 83:4 (2008), 564–572
24.
B. I. Suleimanov, ““Quantizations” of the second Painlevé equation and the problem of the equivalence of its $L$–$A$ pairs”, Theoret. and Math. Phys., 156:3 (2008), 1280–1291
2007
25.
A. M. Il'in, B. I. Suleimanov, “Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe. II. Large values of the parameter $t$”, Sb. Math., 198:9 (2007), 1299–1324
2006
26.
A. M. Il'in, B. I. Suleimanov, “Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe”, Sb. Math., 197:1 (2006), 53–67
27.
B. I. Suleimanov, “On some typical features of motion with damping in the case of smooth inhomogeneity”, Doklady Mathematics, 73, no. 2, 2006, 299–301
A. M. Il'in, B. I. Suleimanov, “Birth of step-like contrast structures connected with a cusp catastrophe”, Sb. Math., 195:12 (2004), 1727–1746
2003
29.
A. M. Il'in, B. I. Suleimanov, “The coefficients of inner asymptotic expansions for solutions of some singular boundary value problems”, Dal'nevost. Mat. Zh., 4:1 (2003), 78–85
2002
30.
A. M. Il'in, B. I. Suleimanov, “On two special functions related to fold singularities”, Doklady Mathematics, 66, no. 3, 2002, 327–329
31.
B. I. Suleimanov, “Cusp catastrophe in slowly varying equilibriums”, Journal of Experimental and Theoretical Physics, 95:5 (2002), 944–956
A. M. Il'in, B. I. Sulei'manov, “On two special functions associated with cusp-type singularities”, Dokl. Akad. Nauk, 387, no. 2, 2002
2001
33.
V. R. Kudashev, B. I. Suleimanov, “The effect of small dissipation on the onset of one-dimensional shock waves”, Journal of Applied Mathematics and Mechanics, 65:3 (2001), 441–451
V. R. Kudashev, B. I. Suleimanov, “Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation”, Theoret. and Math. Phys., 118:3 (1999), 325–332
35.
O. M. Kiselev, B. I. Suleimanov, “The solution of the Painleve equations as special functions of catastrophes, defined by a rejection in these equations of terms with derivative”, 1999, arXiv: solv-int/9902004
1998
36.
V. R. Kudashev, B. I. Suleimanov, “One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model $\Phi^6$: Onset of Nondissipative Shock Waves”, 1998, arXiv: hep-th/9811007
1996
37.
V. Kudashev, B. Suleimanov, “A soft mechanism for the generation of dissipationless shock waves”, Physics Letters A, 221:3 (1996), 204–208
V. R. Kudashev, B. I. Suleimanov, “Characteristic features of some typical spontaneous intensity collapse processes in unstable media”, JETP Letters, 62 (1995), 358
39.
B. I. Suleimanov, “Quantization of two-gap potentials in nonperturbative string theory and oscillations of the Gurevich-Pitaevskii nondissipative shock wave”, Physics of Atomic Nuclei, 58:6 (1995)
1994
40.
S. P. Balandin, B. I. Suleimanov, “Linearization of a Burgers-type system connected with the Hamiltonian structure of second-order ordinary differential equations”, Differ. Equ., 30:12 (1994), 1998–2000
41.
B. I. Suleimanov, “The Hamilton property of Painlevé equations and the method of isomonodromic deformations”, Differ. Equ., 30:5 (1994), 726–732
42.
B. I. Suleimanov, “Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements”, Theoret. and Math. Phys., 98:2 (1994), 132–138
43.
B. I. Suleimanov, “ORIGINATION OF NONDISSIPATIVE SHOCK-WAVES AND NONPERTURBATIVE GRAVITATION THEORY”, ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 105:5 (1994), 1089-1097
1993
44.
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
45.
B. I. Suleimanov, “Solution of the Korteweg-de Vries equation which arises near the breaking point in problems with a slight dispersion”, JETP Letters, 58 (1993), 849–849
1992
46.
B. I. Suleimanov, “A “nonlinear” generalization of special functions of wave catastrophes described by double integrals”, Math. Notes, 52:5 (1992), 1146–1149
1993
47.
B. I. Suleimanov, “The isomonodromic Stokes phenomenon and nonlinear effects near a cuspidal caustic”, Dokl. Math., 46:2 (1993), 220–224
1995
48.
B. I. Suleimanov, “The second Painlevé equation at a problem about nonlinear effects near caustics”, J. Math. Sci., 73:4 (1995), 482–493
1990
49.
B. I. Suleimanov, Differ. Uravn., 26:3 (1990), 540–542
1987
50.
B. I. Suleimanov, “THE RELATION BETWEEN ASYMPTOTIC PROPERTIES OF SOLUTIONS OF THE 2ND PAINLEVE EQUATION IN DIFFERENT DIRECTIONS TOWARDS INFINITY”, Differential Equations, 23:5 (1987), 569-576
1986
51.
B. I. Suleimanov, “On asymptotics of regular solutions for a special kind of Painlevé V equation”, Appendix, 1 (1986), 230–260
1984
52.
V. Yu. Novokshenov, B. I. Suleimanov, “The isomonodromic deformation method and asymptotics of the second and third Painleve transcendents”, Usp. Mat. Nauk, 39:4 (1984), 114–115
A. M. Il'in, B. I. Suleimanov, “The asymptotics of the Green function for a second-order elliptic equation near the boundary of the domain”, Math. USSR-Izv., 23:3 (1984), 579–594
2023
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