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Startsev, Sergey Yakovlevich

Total publications: 27 (27)
in MathSciNet: 16 (16)
in zbMATH: 12 (12)
in Web of Science: 15 (15)
in Scopus: 15 (15)
Cited articles: 17
Citations in Math-Net.Ru: 169
Citations in Web of Science: 136
Citations in Scopus: 113

Number of views:
This page:1088
Abstract pages:4589
Full texts:1335
References:423
Candidate of physico-mathematical sciences (1998)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Phone: +7 (3472) 23 33 42
Website: http://www.researcherid.com/rid/D-1158-2009
Keywords: nonlinear partial differential and difference equations; Darboux integrability; C-integrability; higher symmetries; Miura transformation; differential and difference substitutions.
UDC: 517.957, 517.956.3, 517.972.7, 514.763.85, 517.956.32, 517.929
MSC: 35L70, 35L65, 35L55, 35L05, 35Q53, 35Q58, 37K10, 37K35

Subject:

Conservation laws and symmetry approach for integrable nonlinear equations and systems.

Inside this research area I specialize on Darboux integrable partial differential and difference equations, their generalized Laplace invariants (which provide constructive tests of integrability and substitution existence for hyperbolic equations) and non-point transformations (differential and difference substitutions) for nonlinear equations.

Biography

Graduated from Mathematical Faculty of Bashkiria State University in 1991. Ph. D. thesis was defended in 1998.

   
Main publications:
  1. S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
  2. V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, Theoret. and Math. Phys., 155:2 (2008), 802–811  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
  3. S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  4. V. E. Adler, S. Ya. Startsev, “Discrete analogues of the Liouville equation”, Theoret. and Math. Phys., 121:2 (1999), 1484–1495  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  5. S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

http://www.mathnet.ru/eng/person17858
http://scholar.google.com/citations?user=c22ZMFIAAAAJ&hl=en
http://zbmath.org/authors/?q=ai:startsev.sergey-ya
https://mathscinet.ams.org/mathscinet/MRAuthorID/600545
http://elibrary.ru/author_items.asp?authorid=14812
http://orcid.org/0000-0001-5891-6191
http://www.researcherid.com/rid/D-1158-2009
http://www.scopus.com/authid/detail.url?authorId=6701643187
https://arxiv.org/a/startsev_s_1

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2019
1. S. Ya. Startsev, “Conservation laws for hyperbolic equations: search algorithm for local preimage with respect to the total derivative”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 85–92  mathnet

   2018
2. S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 110–119  mathnet  mathscinet
3. S. Ya. Startsev., “O mnogokomponentnykh differentsialnykh podstanovkakh”, Mezhdunarodnaya nauchnaya konferentsiya “Spektralnaya teoriya i smezhnye voprosy”. Sbornik tezisov (Ufa, 1–4 oktyabrya 2018 g.), Izd-vo BGPU, Ufa, 2018, 148–150
4. S. Ya. Startsev, “Neobkhodimoe uslovie integriruemosti po Darbu dlya poludiskretnykh avtonomnykh uravnenii lineinykh po proizvodnym”, Sovremennye problemy fiziko-matematicheskikh nauk. Materialy IV Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Orel, 22-25 noyabrya 2018 g.), Chast 1, OGU, Orel, 2018, 79–82
5. S. Ya. Startsev, “Struktura mnozhestva simmetrii giperbolicheskikh sistem liuvillevskogo tipa i obobschennye invarianty Laplasa”, Ufimsk. matem. zhurn., 10:4 (2018), 103–110  mathnet
6. S. Ya. Startsev, “Structure of set of symmetries for hyperbolic systems of Liouville type and generalized Laplace invariants”, Ufa Math. J., 10:4 (2018), 103–110  mathnet  crossref  isi

   2017
7. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 34 , 20 pp., arXiv: 1511.09418  mathnet (cited: 1)  crossref  isi (cited: 1)  scopus (cited: 1)
8. S. Ya. Startsev, “On relationships between symmetries depending on arbitrary functions and integrals of discrete equations”, Journal of Physics A: Mathematical and Theoretical, 50:50 (2017), 50LT01 , 12 pp., arXiv: 1611.02235  crossref  isi (cited: 1)  scopus (cited: 1)
9. S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. Journal, 9:4 (2017), 108–113  mathnet  crossref  isi  elib  scopus
10. S.Ya. Startsev, “Parametrizovannye proizvolnymi funktsiyami semeistva simmetrii i formalnye integraly diskretnykh uravnenii”, Mezhdunarodnaya matematicheskaya konferentsiya po teorii funktsii, posvyaschennaya 100-letiyu chl.-korr. AN SSSR A.F. Leonteva. Sbornik tezisov (g. Ufa, 24 - 27 maya 2017 g.), RITs BashGU, Ufa, 2017, 151-152  elib
11. Startsev S. Ya., “The degeneracy of Laplace invariants for hyperbolic systems possessing integrals”, Sovremennye problemy fiziko-matematicheskikh nauk. Materialy III Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Orel, 23-26 noyabrya 2017 g.), eds. T.N. Mozharova, OGU, Orel, 2017, 96-99 arXiv:1710.11068  elib

   2016
12. Startsev S. Ya., “Formalnye integraly i operatory Neter giperbolicheskikh sistem uravnenii, dopuskayuschikh bogatyi nabor simmetrii”, Ufimskaya matematicheskaya konferentsiya s mezhdunarodnym uchastiem, Sbornik tezisov (g. Ufa, 27–30 sentyabrya 2016 goda), RITs BashGU, g. Ufa, 2016, 152-153  elib

   2014
13. Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 66–13  mathnet (cited: 1)  crossref  mathscinet  isi (cited: 1)  elib  scopus
14. S. Ya. Startsev, “Darboux integrable discrete equations possessing an autonomous first-order integral”, Journal of Physics A: Mathematical and Theoretical, 47:10 (2014), 105204 , 16 pp.  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 2)  scopus (cited: 6)

   2012
15. S. Ya. Startsev, “Darboux integrable differential-difference equations admitting a first-order integral”, Ufa Mathematical Journal, 4:3 (2012), 159-173  mathnet  mathnet  mathscinet  elib

   2011
16. S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Mathematical Journal, 3:1 (2011), 78–82  mathnet  mathscinet  zmath  elib

   2010
17. Sergey Ya. Startsev, “On Non-Point Invertible Transformations of Difference and Differential-Difference Equations”, SIGMA, 6 (2010), 92–14  mathnet (cited: 10)  crossref  mathscinet  isi (cited: 9)  elib (cited: 7)  scopus (cited: 9)

   2008
18. S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 4)
19. V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, Theoret. and Math. Phys., 155:2 (2008), 802–811  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 11)  elib (cited: 7)  elib (cited: 7)  scopus (cited: 10)
20. S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

   2006
21. D. K. Demskoi, S. Ya. Startsev, “On construction of symmetries from integrals of hyperbolic partial differential systems”, J. Math. Sci., 136:6 (2006), 4378–4384  mathnet  crossref  mathscinet  zmath  elib (cited: 6)  elib (cited: 6)  scopus (cited: 9)

   2003
22. A. V. Zhiber, S. Ya. Startsev, “Integrals, Solutions, and Existence Problems for Laplace Transformations of Linear Hyperbolic Systems”, Math. Notes, 74:6 (2003), 803–811  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 13)  elib (cited: 21)  scopus (cited: 8)

   2001
23. S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 5)  scopus (cited: 5)

   1999
24. V. E. Adler, S. Ya. Startsev, “Discrete analogues of the Liouville equation”, Theoret. and Math. Phys., 121:2 (1999), 1484–1495  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 47)  elib (cited: 36)  scopus (cited: 42)
25. S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 4)  scopus (cited: 5)

   1998
26. S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 12)  elib (cited: 10)  scopus (cited: 11)

   1995
27. A. V. Zhiber, V. V. Sokolov, S. Ya. Startsev, “On nonlinear Darboux-integrable hyperbolic equations”, Doklady Math., 53:1 (1995), 128-130  mathnet  mathscinet  zmath  isi (cited: 4)

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