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Sharipov, Ruslan Abdulovich

 Statistics Math-Net.Ru 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 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      ; 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    ; Ufa Math. J., 7:3 (2015), 95–107 4. R. A. Sharipov, “On a problem associated with approximation by exponential functions”, Ufimsk. Mat. Zh., 7:1 (2015),  86–97    ; Ufa Math. J., 7:1 (2015), 83–94 2012 5. R. A. Sharipov, “Perfect cuboids and irreducible polynomials”, Ufimsk. Mat. Zh., 4:1 (2012),  153–160 2010 6. R. A. Sharipov, “A counterexample to Khabibullin's conjecture for integral inequalities”, Ufimsk. Mat. Zh., 2:4 (2010),  99–107 2007 7. R. A. Sharipov, “Êèíåìàòèêà, äèíàìèêà è òåðìîäèíàìèêà ïëàñòè÷íîñòè â íåëèíåéíîé òåîðèè äåôîðìàöèé”, Matem. Mod. Kraev. Zadachi, 1 (2007),  276–279 2002 8. R. A. Sharipov, “Dynamic Systems Admitting the Normal Shift and Wave Equations”, TMF, 131:2 (2002),  244–260        ; Theoret. and Math. Phys., 131:2 (2002), 651–665 2001 9. R. A. Sharipov, “Newtonian normal shift in multidimensional Riemannian geometry”, Mat. Sb., 192:6 (2001),  105–144        ; Sb. Math., 192:6 (2001), 895–932 10. R. A. Sharipov, “Newtonian dynamical systems admitting normal blow-up of points”, Zap. Nauchn. Sem. POMI, 280 (2001),  278–298      ; 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    ; 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      ; Math. Notes, 68:2 (2000), 255–262 13. A. V. Gladkov, V. V. Dmitrieva, R. A. Sharipov, “Some nonlinear equations reducible to diffusion-type equations”, TMF, 123:1 (2000),  26–37      ; Theoret. and Math. Phys., 123:1 (2000), 436–445 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      ; 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 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      ; Funct. Anal. Appl., 30:1 (1996), 15–22 17. E. V. Ferapontov, R. A. Sharipov, “On first-order conservation laws for systems of hydronamic type equations”, TMF, 108:1 (1996),  109–128      ; Theoret. and Math. Phys., 108:1 (1996), 937–952 1995 18. R. A. Sharipov, “Metrizability of dynamical systems by a conformally equivalent metric”, TMF, 103:2 (1995),  276–282      ; Theoret. and Math. Phys., 103:2 (1995), 556–560 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      ; Theoret. and Math. Phys., 103:2 (1995), 550–555 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      ; Theoret. and Math. Phys., 103:2 (1995), 543–549 1994 21. A. Yu. Boldin, R. A. Sharipov, “Dynamical systems that admit normal shift”, Dokl. Akad. Nauk, 334:2 (1994),  165–167      ; 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      ; Theoret. and Math. Phys., 101:1 (1994), 1218–1223 23. A. Yu. Boldin, R. A. Sharipov, “Multidimensional dynamical systems accepting the normal shift”, TMF, 100:2 (1994),  264–269      ; Theoret. and Math. Phys., 100:2 (1994), 997–1000 1993 24. A. Yu. Boldin, R. A. Sharipov, “Dynamical systems that admit normal displacement”, TMF, 97:3 (1993),  386–395      ; Theoret. and Math. Phys., 97:3 (1993), 1364–1369 25. S. S. Safin, R. A. Sharipov, “Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$”, TMF, 95:1 (1993),  146–159      ; 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      ; Theoret. and Math. Phys., 87:1 (1991), 363–369 1990 27. R. A. Sharipov, “Integration of Bogoyavlenskii chains”, Mat. Zametki, 47:1 (1990),  157–160      ; Math. Notes, 47:1 (1990), 101–103 28. I. Yu. Cherdantsev, R. A. Sharipov, “Finite-gap solutions of the Bullough–Dodd–Zhiber–Shabat equation”, TMF, 82:1 (1990),  155–160      ; Theoret. and Math. Phys., 82:1 (1990), 108–11 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      ; Theoret. and Math. Phys., 78:3 (1989), 244–252 1987 30. R. A. Sharipov, “Soliton multiplets of the Kortweg–de Vries equation”, Dokl. Akad. Nauk SSSR, 292:6 (1987),  1356–1359 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      ; Russian Math. Surveys, 42:5 (1987), 177–178 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      ; Russian Math. Surveys, 41:5 (1986), 165–166 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  ; Ufa Math. J., 12:3 (2020), 119–120

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