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Sharipov, Ruslan Abdulovich

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Total publications: 33
Scientific articles: 32

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Associate professor
Candidate of physico-mathematical sciences (1989)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 22.04.1961
E-mail:
Website: http://ruslan-sharipov.ucoz.com
Keywords: dynamical systems on manifolds; integrable equations of mathematical physics; classificational theory of ordinary differential equations; algebraicity of holomorphic functions.

Subject:

I have interests in several brunches of mathematics and in theoretical physics. Part of these interests are already realized and supported by obtained results. Another part is reserved as future prospect. To the first part of my interests I attribute 1) soliton theory, theory of soliton equations, and theory of integrable dynamical systems in whole; 2) classification problems for differential equations being solved by geometric methods (point transformations, symmetry analysis, invariants search, and invariant form of integrability conditions); 3) complex analysis on a joint with algebra; 4) differential geometry on a joint with theory of dynamical systems (the construction of normal shift). Second part of my scientific interests is elementary particle physics and field theory. I am going to concentrate efforts in this direction in order to raise my level of competence and to obtain some results here in future.

Biography

In 1983 I graduated Moscow Institute of Physics and Technology (MIPT), department of General and Applied Physics with specialization in solid state physics. However, further I entered Post Graduate Courses at Steklov Mathematical Institute of Academy of Sciences of USSR and continued my career in the field of mathematics. Here I specialized in the field of soliton equations. I have obtained explicit formulas for multiplet solutions of Korteweg–de Vries equation and Kadomtsev–Petviashvili equation either in rational case and in the case of such solutions with finite-gap (algebro-geometrical) background. This was subject of my Ph.D. thesis, which was defended in 1989. Since 1987 up to now I am applied in Bashkir State University at the Chair of Algebra and Geometry. In 1987 in cooperation with R. F. Bikbaev I have managed to transfer one-dimensional scattering theory, which is used for solving Korteweg–de Vries equation, to the case of potentials fast decreasing to finite-gap (algebro-geometrical) background. Large time asymptotics for corresponding solutions of Korteweg–de Vries equation also was described. Further I dealt with Bullough–Dodd–Jiber–Shabat equation, which now is also called Tzitzeica equation. In cooperation with I. Yu. Cherdantsev I have constructed finite-gap (algebro-geometrical) solutions for this equation and soliton solutions on finite-gap background as well. In cooperation with R. I. Yamilov I have rediscovered Backlund transformations for this equation, which was first discovered by Tzitzeica in the beginning of twentieth century, then forgotten, and assumed to be absent by specialists. In 1993 my interests moved to the field of differential geometry. In cooperation with A. Yu. Boldin I have generalized classical construction of normal shift by Bonnet for the case of shift along trajectories of Newtonian dynamical systems. Then in cooperation with A. A. Bronnikov, V. V. Dmitrieva, and S. S. Safin these result was transferred into Riemannian geometry. I am continuing these investigations up to now. Moreover, since 1993 I have obtained effective criterion for point classification for one class of ordinary differential equations, in cooperation with M. V. Pavlov and S. I. Svinolupov I have obtained invariant criterion of integrability for the equations solvable by generalized hodograph method suggested by S. P. Tsarev. I have also some results on algebraicity of holomorphic functions in cooperation with A. B. Sukhov and E. N. Tsyganov. In 1999 I have prepared a thesis for the degree of Doctor of Sciences in Russia. However, this thesis is not yet defended.

In 1998 I have won grant from G. Soros foundation and I was awarded a title of Soros Associate Professor.

   
Main publications:
  • Sharipov R. A. Effective procedure of point-classification for the equation $y''=P+3Qy'+3Ry'^2+Sy'^3$, Electronic archive at LANL (http://arXiv.org), 1998, math.DG/9802027, 1–35.

http://www.mathnet.ru/eng/person8762
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
2018
1. R. A. Sharipov, “Symmetry-Based Approach to the Problem of a Perfect Cuboid”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152 (2018),  143–158  mathnet  mathscinet
2017
2. R. A. Sharipov, “Multiple discriminants and extreme values of polynomials of several variables”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 143 (2017),  87–94  mathnet  mathscinet  zmath; Journal of Mathematical Sciences, 245:1 (2020), 89–97
2015
3. R. A. Sharipov, “Asymptotic approach to the perfect cuboid problem”, Ufimsk. Mat. Zh., 7:3 (2015),  100–113  mathnet  elib; Ufa Math. J., 7:3 (2015), 95–107  isi  scopus
4. R. A. Sharipov, “On a problem associated with approximation by exponential functions”, Ufimsk. Mat. Zh., 7:1 (2015),  86–97  mathnet  elib; Ufa Math. J., 7:1 (2015), 83–94  isi  scopus
2012
5. R. A. Sharipov, “Perfect cuboids and irreducible polynomials”, Ufimsk. Mat. Zh., 4:1 (2012),  153–160  mathnet
2010
6. R. A. Sharipov, “A counterexample to Khabibullin's conjecture for integral inequalities”, Ufimsk. Mat. Zh., 2:4 (2010),  99–107  mathnet  zmath  elib
2007
7. R. A. Sharipov, “Кинематика, динамика и термодинамика пластичности в нелинейной теории деформаций”, Matem. Mod. Kraev. Zadachi, 1 (2007),  276–279  mathnet
2002
8. R. A. Sharipov, “Dynamic Systems Admitting the Normal Shift and Wave Equations”, TMF, 131:2 (2002),  244–260  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 131:2 (2002), 651–665  isi
2001
9. R. A. Sharipov, “Newtonian normal shift in multidimensional Riemannian geometry”, Mat. Sb., 192:6 (2001),  105–144  mathnet  mathscinet  zmath  elib; Sb. Math., 192:6 (2001), 895–932  isi  scopus
10. R. A. Sharipov, “Newtonian dynamical systems admitting normal blow-up of points”, Zap. Nauchn. Sem. POMI, 280 (2001),  278–298  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 119:2 (2004), 281–291
2000
11. O. N. Mikhailov, R. A. Sharipov, “The geometry of point extensions of a class of second-order differential equations”, Differ. Uravn., 36:10 (2000),  1331–1335  mathnet  mathscinet; Differ. Equ., 36:10 (2000), 1469–1474
12. R. A. Sharipov, E. N. Ciganov, “Separate algebraicity along families of algebraic curves”, Mat. Zametki, 68:2 (2000),  294–302  mathnet  mathscinet  zmath; Math. Notes, 68:2 (2000), 255–262  isi
13. A. V. Gladkov, V. V. Dmitrieva, R. A. Sharipov, “Some nonlinear equations reducible to diffusion-type equations”, TMF, 123:1 (2000),  26–37  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 123:1 (2000), 436–445  isi
1998
14. A. Yu. Boldin, R. A. Sharipov, “On the solution of normality equations in dimension $n\ge 3$”, Algebra i Analiz, 10:4 (1998),  37–61  mathnet  mathscinet  zmath; St. Petersburg Math. J., 10:4 (1999), 603–618
1996
15. A. B. Sukhov, R. A. Sharipov, “On the algebraicity of holomorphic mappings”, Dokl. Akad. Nauk, 350:4 (1996),  453–454  mathnet  mathscinet  zmath
16. M. V. Pavlov, S. I. Svinolupov, R. A. Sharipov, “Invariant Integrability Criterion for Equations of Hydrodynamic Type”, Funktsional. Anal. i Prilozhen., 30:1 (1996),  18–29  mathnet  mathscinet  zmath; Funct. Anal. Appl., 30:1 (1996), 15–22  isi
17. E. V. Ferapontov, R. A. Sharipov, “On first-order conservation laws for systems of hydronamic type equations”, TMF, 108:1 (1996),  109–128  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 108:1 (1996), 937–952  isi
1995
18. R. A. Sharipov, “Metrizability of dynamical systems by a conformally equivalent metric”, TMF, 103:2 (1995),  276–282  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 103:2 (1995), 556–560  isi
19. A. Yu. Boldin, A. A. Bronnikov, V. V. Dmitrieva, R. A. Sharipov, “Complete normality conditions for the dynamical systems on Riemannian manifolds”, TMF, 103:2 (1995),  267–275  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 103:2 (1995), 550–555  isi
20. A. Yu. Boldin, V. V. Dmitrieva, S. S. Safin, R. A. Sharipov, “Dynamical systems on a Riemannian manifold that admit normal shift”, TMF, 103:2 (1995),  256–266  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 103:2 (1995), 543–549  isi
1994
21. A. Yu. Boldin, R. A. Sharipov, “Dynamical systems that admit normal shift”, Dokl. Akad. Nauk, 334:2 (1994),  165–167  mathnet  mathscinet  zmath; Dokl. Math., 39:1 (1994), 49–51
22. R. A. Sharipov, “The problem of metrizability of dynamical systems that admit normal shift”, TMF, 101:1 (1994),  85–93  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 101:1 (1994), 1218–1223  isi
23. A. Yu. Boldin, R. A. Sharipov, “Multidimensional dynamical systems accepting the normal shift”, TMF, 100:2 (1994),  264–269  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 100:2 (1994), 997–1000  isi
1993
24. A. Yu. Boldin, R. A. Sharipov, “Dynamical systems that admit normal displacement”, TMF, 97:3 (1993),  386–395  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 97:3 (1993), 1364–1369  isi
25. S. S. Safin, R. A. Sharipov, “Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$”, TMF, 95:1 (1993),  146–159  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 95:1 (1993), 462–470
1991
26. R. A. Sharipov, “Minimal tori in the five-dimensional sphere in $\mathbb C^3$”, TMF, 87:1 (1991),  48–56  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 87:1 (1991), 363–369  isi
1990
27. R. A. Sharipov, “Integration of Bogoyavlenskii chains”, Mat. Zametki, 47:1 (1990),  157–160  mathnet  mathscinet  zmath; Math. Notes, 47:1 (1990), 101–103  isi
28. I. Yu. Cherdantsev, R. A. Sharipov, “Finite-gap solutions of the Bullough–Dodd–Zhiber–Shabat equation”, TMF, 82:1 (1990),  155–160  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 82:1 (1990), 108–11  isi
1989
29. R. F. Bikbaev, R. A. Sharipov, “Asymptotics at $t\to\infty$ of the solution to the Cauchy problem for the Korteweg–de Vries equation in the class of potentials with finite-gap behavior as $x\to\pm\infty$”, TMF, 78:3 (1989),  345–356  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 78:3 (1989), 244–252  isi
1987
30. R. A. Sharipov, “Soliton multiplets of the Kortweg–de Vries equation”, Dokl. Akad. Nauk SSSR, 292:6 (1987),  1356–1359  mathnet  mathscinet  zmath
31. R. A. Sharipov, “Multiplet solutions of the Kadomtsev–Petviashvili equation against a finite-zone background”, Uspekhi Mat. Nauk, 42:5(257) (1987),  221–222  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:5 (1987), 177–178  isi
1986
32. R. A. Sharipov, “Finite-zone analogues of $N$-multiplet solutions of the Korteweg–de Vries equation”, Uspekhi Mat. Nauk, 41:5(251) (1986),  203–204  mathnet  mathscinet  zmath; Russian Math. Surveys, 41:5 (1986), 165–166  isi

2020
33. 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”, Ufimsk. Mat. Zh., 12:2 (2020),  118–119  mathnet; Ufa Math. J., 12:3 (2020), 119–120

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