arXiv subjects
Publications and source records attributed to Arthur G. Sergheyev.
We present a simple way of generating the infinite set of Jacobi tensors, compatible with a given one, via the "gauge transformations" of the functions on Jacobi manifold. We consider also some applications of this result to the construction of bi-Hamiltonian systems on Jacobi manifolds.
We show that the number of symmetry operators of order not higher that q of the nonstationary n-dimensional (n=1,2,3,4) Schroedinger equation (SE) with nonvanishing potentials is finite and does not exceed that of SE with zero potentials for arbitrary q=0,1,2,... . This result is applied for the determination of the general form of time dependance of the symmetry operators of SE with time-independant potentials.
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered. We establish when there exist generalized symmetries from these subspaces, which depend from the above-mentioned variables.
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we explicitly determine the dependance of coefficients of generalized symmetries from these subspaces on the above-mentioned variables. We establish the connection of our results with the theory of quasiexactly solvable models. Some generalizations of the approach proposed also are discussed.