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)
