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
V. E. Adler, S. Ya. Startsev, “Discrete analogues of the Liouville equation”, Theoret. and Math. Phys., 121:2 (1999), 1484–1495
2.
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
3.
A. V. Zhiber, V. V. Sokolov, S. Ya. Startsev, “On nonlinear Darboux-integrable hyperbolic equations”, Doklady Math., 53:1 (1995), 128-130
4.
S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010
5.
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
7.
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
8.
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
9.
S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018
10.
S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470
11.
S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253
12.
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
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
17.
S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Mathematical Journal, 3:1 (2011), 78–82
18.
Ufa Math. J., 13:2 (2021), 160–169
19.
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
20.
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
24.
S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, J. Math. Sci. (N. Y.), 252:2 (2021), 232–241
25.
S. Ya. Startsev, Pre-Hamiltonian operators related to hyperbolic equations of Liouville type, 2020 , 11 pp., arXiv: 2002.10442
26.
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
27.
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
28.
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
29.
S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. Journal, 9:4 (2017), 108–113
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
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