The theory of transformations for hyperbolic second-order equations in the plane, developed by Darboux, Laplace and Moutard, has many applications in classical differential geometry [12, 13], andâ€¦ (More)

We characterize non-degenerate Lagrangians of the form âˆ« f(ux, uy, ut) dx dy dt such that the corresponding Euler-Lagrange equations (fux)x +(fuy )y +(fut)t = 0 are integrable by the method ofâ€¦ (More)

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of suchâ€¦ (More)

We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes theâ€¦ (More)

We classify all integrable 3-dimensional scalar discrete quasilinear equations Q3 = 0 on an elementary cubic cell of the lattice Z 3. An equation Q3 = 0 is called integrable if it may be consistentlyâ€¦ (More)

was initiated by Dubrovin and Novikov [2] and continued by Mokhov and Ferapontov [5]. In the present paper, we prove a theorem on the existence of three Hamiltonian structures for a diagonalizableâ€¦ (More)

We classify all integrable three-dimensional scalar discrete affine linear equations Q3 = 0 on an elementary cubic cell of the lattice Z3. An equation Q3 = 0 is called integrable if it may beâ€¦ (More)

We investigate second order quasilinear equations of the form fijuxixj = 0, where u is a function of n independent variables x1, ..., xn, and the coefficients fij depend on the first orderâ€¦ (More)

A new method to identify all sufficiently long repeating substrings in one or several symbol sequences is proposed. The method is based on a specific gauge applied to symbol sequences that guaranteesâ€¦ (More)