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:
S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106
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
S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470
V. E. Adler, S. Ya. Startsev, “Discrete analogues of the Liouville equation”, Theoret. and Math. Phys., 121:2 (1999), 1484–1495
S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018
S. Ya. Startsev, “On Bäcklund Transformations Preserving the Darboux Integrability of Hyperbolic Equations”, Lobachevskii J. Math., 44:5 (2023), 1929–1937
Startsev S.Y., “Conservation Laws for Hyperbolic Equations: Search Algorithm for Local Preimage with Respect to the Total Derivative”, Journal of Mathematical Sciences (United States), 257:3 (2021), 358–365
6.
S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, J. Math. Sci. (N. Y.), 252:2 (2021), 232–241
2020
7.
S. Ya. Startsev, Pre-Hamiltonian operators related to hyperbolic equations of Liouville type, 2020 , 11 pp., arXiv: 2002.10442
2021
8.
S. Ya. Startsev, “Conservation Laws for Hyperbolic Equations: Search Algorithm for Local Preimage with Respect to the Total Derivative”, J. Math. Sci. (N. Y.), 257:3 (2021), 358–365
9.
S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, J. Math. Sci. (N. Y.), 252:2 (2021), 232–241
2018
10.
S. Ya. Startsev, “Neobkhodimoe uslovie integriruemosti po Darbu dlya poludiskretnykh avtonomnykh uravnenii lineinykh po proizvodnym”, statya v sbornike trudov konferentsii, Sovremennye problemy fiziko-matematicheskikh nauk. Materialy IV Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Orel, 22-25 noyabrya 2018 g.), Chast 1, OGU, Orel, 2018, 79–82
11.
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
12.
S. Ya. Startsev., “O mnogokomponentnykh differentsialnykh podstanovkakh”, Mezhdunarodnaya nauchnaya konferentsiya “Spektralnaya teoriya i smezhnye voprosy”. Sbornik trudov (Ufa, 1–4 oktyabrya 2018 g.), Izd-vo BGPU, Ufa, 2018, 148–150
2017
13.
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
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, December (2017), 50LT01 , 12 pp., arXiv: 1611.02235
Startsev S. Ya., “The degeneracy of Laplace invariants for hyperbolic systems possessing integrals”, statya v sbornike trudov konferentsii, Sovremennye problemy fiziko-matematicheskikh nauk. Materialy III
Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Orel, 23-26 noyabrya 2017 g.), eds. T.N. Mozharova, OGU, Orel, 2017 (dekabr), 96-99arXiv:1710.11068
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.
S. Ya. Startsev, “Darboux integrable differential-difference equations admitting a first-order integral”, Ufa Mathematical Journal, 4:3 (2012), 159-173
2011
22.
S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Mathematical Journal, 3:1 (2011), 78–82
2010
23.
Sergey Ya. Startsev, “On Non-Point Invertible Transformations of Difference and Differential-Difference Equations”, SIGMA, 6 (2010), 92–14
S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106
25.
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
26.
S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253
2006
27.
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
2003
28.
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
2001
29.
S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470
1999
30.
V. E. Adler, S. Ya. Startsev, “Discrete analogues of the Liouville equation”, Theoret. and Math. Phys., 121:2 (1999), 1484–1495
31.
S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018
1998
32.
S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010
1995
33.
A. V. Zhiber, V. V. Sokolov, S. Ya. Startsev, “On nonlinear Darboux-integrable hyperbolic equations”, Doklady Math., 53:1 (1995), 128-130
2023
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