An extension of the Noether theorem: Accompanying equations possessing conservation laws. - Vladimir A. Dorodnitsyn; Nail H. Ibragimov (Commun. Nonlinear Sci. Numer. Simul., 2014)

One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: Symmetry classification, conservation laws, difference schemes. - Vladimir A. Dorodnitsyn; Roman Kozlov; Sergey V. Meleshko (Commun. Nonlinear Sci. Numer. Simul., 2019)

Shallow water equations in Lagrangian coordinates: Symmetries, conservation laws and its preservation in difference models. - Vladimir A. Dorodnitsyn; Evgenii I. Kaptsov (Commun. Nonlinear Sci. Numer. Simul., 2020)

Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates. - Vladimir A. Dorodnitsyn; Evgenii I. Kaptsov (CoRR, 2020)

One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes. - Vladimir A. Dorodnitsyn; Roman Kozlov; Sergey V. Meleshko (CoRR, 2020)

Conservative invariant finite-difference schemes for the modified shallow water equations in Lagrangian coordinates. - Vladimir A. Dorodnitsyn; Evgenii I. Kaptsov; Sergey V. Meleshko (CoRR, 2021)

Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations. - Vladimir A. Dorodnitsyn; Evgenii I. Kaptsov (CoRR, 2021)

Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates. - Evgenii I. Kaptsov; Vladimir A. Dorodnitsyn (CoRR, 2023)

Lie group symmetry analysis and invariant difference schemes of the two-dimensional shallow water equations in Lagrangian coordinates. - Vladimir A. Dorodnitsyn; Evgenii I. Kaptsov; Sergey V. Meleshko (Commun. Nonlinear Sci. Numer. Simul., 2023)

Invariant finite-difference schemes for cylindrical one-dimensional MHD flows with conservation laws preservation. - Evgenii I. Kaptsov; Vladimir A. Dorodnitsyn; Sergey V. Meleshko (Commun. Nonlinear Sci. Numer. Simul., 2023)

Symmetry-Preserving Finite-Difference Schemes and Auto-Bäcklund Transformations for the Schwarz Equation. - Evgenii I. Kaptsov; Vladimir A. Dorodnitsyn (CoRR, 2025)