105 citations · 137 across the 10 of their papers we have counts for
10 papers
Pre-Hamiltonian operators related to hyperbolic equations of Liouville type
S. Ya. Startsev
This text is devoted to hyperbolic equations admitting differential operators that map any function of one independent variable into a symmetry of the corresponding equation. We us…
The degeneracy of Laplace invariants for hyperbolic systems possessing integrals
S. Ya. Startsev
A direct generalization of Laplace invariants to the case of hyperbolic partial differential systems is considered. The proof of the following statement is given: the determinant o…
On relationships between symmetries depending on arbitrary functions and integrals of discrete equations
S. Ya. Startsev
The paper is devoted to the conjecture that an equation is Darboux integrable if and only if it possesses symmetries depending on arbitrary functions. We note that results of previ…
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries
Sergey Ya. Startsev
The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any func…
Non-Point Invertible Transformations and Integrability of Partial Difference Equations
Sergey Ya. Startsev
This article is devoted to the partial difference quad-graph equations that can be represented in the form , where the map $(w,z) \righta…
Darboux integrable discrete equations possessing an autonomous first-order integral
S. Ya. Startsev
All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics…