30 citations · 63 across the 11 of their papers we have counts for
4 papers · 1 filter
Invariant Conservation Law-Preserving Discretizations of Linear and Nonlinear Wave Equations
A. F. Cheviakov, V. A. Dorodnitsyn, E. I. Kaptsov
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, u…
Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
V. A. Dorodnitsyn, E. I. Kaptsov
The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangi…
Analysis of the One-dimensional Euler-Lagrange equation of continuum mechanics with a Lagrangian of a special form
E. I. Kaptsov, S. V. Meleshko
Flows of one-dimensional continuum in Lagrangian coordinates are studied in the paper. Equations describing these flows are reduced to a single Euler-Lagrange equation which contai…
First integrals of ordinary difference equations which do not possess a variational formulation
P. Winternitz, V. Dorodnitsyn, E. Kaptsov +1
The paper presents a new method for finding first integrals of ordinary difference equations which do not possess Lagrangians, nor Hamiltonians. As an example we solve a third orde…