Geometric methods of integration of differential equations, computer algebra.
Main publications:
S. P. Tsarev, “Generalized Laplace transformations and integration of hyperbolic systems of linear partial differential equations”, Proceedings of 2005 International Symposium on Symbolic and Algebraic Computation (Beijing, July 2005), ACM Press, NY, 2005, 325–331
S. P. Tsarev, “The geometry of hamiltonian systems of hydrodynamic type. The generalized hodograph method”, Mathematics of the USSR-Izvestiya, 37:2 (1990), 397–419
S. P. Tsarev, “Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations”, Theoretical and Mathematical Physics, 122:1 (2000), 121–133
E. V. Ferapontov , K. R. Khusnutdinova, S. P. Tsarev, “On a Class of Three-Dimensional Integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243
I. A. Taimanov, S. P. Tsarev, “Two-dimensional Schrodinger operators with fast decaying potential and multidimensional $L_2$-kernel”, Russian Mathematical Surveys, 62:3 (2008) (to appear)
Sergey P. Tsarev, Valery V. Denisenko, Marat M. Valikhanov, “Multidimensional free interpolation framework for high-precision modeling of slant total electron contents in mid-latitude and equatorial regions”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 781–791
2017
2.
S. P. Tsarev, V. A. Stepanenko, “On weakly commutative triples of partial differential operators”, Sib. Èlektron. Mat. Izv., 14 (2017), 1050–1063
2014
3.
R. G. Novikov, I. A. Taimanov, S. P. Tsarev, “Two-Dimensional von Neumann–Wigner Potentials with a Multiple Positive Eigenvalue”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 74–77; Funct. Anal. Appl., 48:4 (2014), 295–297
I. A. Taimanov, S. P. Tsarev, “Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation”, TMF, 176:3 (2013), 408–416; Theoret. and Math. Phys., 176:3 (2013), 1176–1183
I. A. Taimanov, S. P. Tsarev, “On the Moutard transformation and its applications to spectral theory and soliton equations”, CMFD, 35 (2010), 101–117; Journal of Mathematical Sciences, 170:3 (2010), 371–387
S. P. Tsarev, E. S. Shemyakova, “Differential Transformations of Parabolic Second-Order Operators in the Plane”, Trudy Mat. Inst. Steklova, 266 (2009), 227–236; Proc. Steklov Inst. Math., 266 (2009), 219–227
I. A. Taimanov, S. P. Tsarev, “Two-dimensional rational solitons and their blowup via the Moutard
transformation”, TMF, 157:2 (2008), 188–207; Theoret. and Math. Phys., 157:2 (2008), 1525–1541
I. A. Taimanov, S. P. Tsarev, “Two-dimensional Schrödinger operators with fast decaying potential and multidimensional $L_2$-kernel”, Uspekhi Mat. Nauk, 62:3(375) (2007), 217–218; Russian Math. Surveys, 62:3 (2007), 631–633
M. V. Pavlov, S. P. Tsarev, “Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 38–54; Funct. Anal. Appl., 37:1 (2003), 32–45
S. P. Tsarev, “Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations”, TMF, 122:1 (2000), 144–160; Theoret. and Math. Phys., 122:1 (2000), 121–133
E. I. Ganzha, S. P. Tsarev, “An algebraic formula for superposition and the completeness of the Bäcklund transformations of $(2+1)$-dimensional integrable systems”, Uspekhi Mat. Nauk, 51:6(312) (1996), 197–198; Russian Math. Surveys, 51:6 (1996), 1200–1202
E. V. Ferapontov, S. P. Tsarev, “Systems of hydrodynamic type, arising in gas chromatography. Riemann invariants and exact solutions”, Matem. Mod., 3:2 (1991), 82–91
M. V. Pavlov, S. P. Tsarev, “On conservation laws of Benney equations”, Uspekhi Mat. Nauk, 46:4(280) (1991), 169–170; Russian Math. Surveys, 46:4 (1991), 196–197
S. P. Tsarev, “The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method”, Izv. Akad. Nauk SSSR Ser. Mat., 54:5 (1990), 1048–1068; Math. USSR-Izv., 37:2 (1991), 397–419
S. P. Tsarev, “The Hamilton property of stationary and inverse equations of condensed matter mechanics and mathematical physics”, Mat. Zametki, 46:1 (1989), 105–111; Math. Notes, 46:1 (1989), 569–573
S. P. Tsarev, “On the Liouville Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov–Whitham averaging theory”, Uspekhi Mat. Nauk, 39:6(240) (1984), 209–210; Russian Math. Surveys, 39:6 (1984), 227–228
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