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.
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
