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On invariant solutions of the equation of non-linear heat conduction with a source

- V. Dorodnitsyn
- Mathematics
- 1982

Applications of Lie Groups to Difference Equations

- V. Dorodnitsyn
- Mathematics
- 1 December 2010

Preface Introduction Brief introduction to Lie group analysis of differential equations Preliminaries: Heuristic approach in examples Finite Differences and Transformation Groups in Space of Discrete… Expand

Invariance and first integrals of continuous and discrete Hamiltonian equations

- V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 10 June 2009

The relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations is considered. The observation that canonical Hamiltonian… Expand

Noether-type theorems for difference equations

- V. Dorodnitsyn
- Mathematics
- 1 December 2001

Abstract The Noether's type constructions for difference functionals, difference equations and meshes (lattices) are reviewed. It is shown in Dorodnitsyn [J. Soviet Math. 55 (1999) 1490]; [Dokl.… Expand

Continuous symmetries of Lagrangians and exact solutions of discrete equations

- V. Dorodnitsyn, R. Kozlov, P. Winternitz
- Physics, Mathematics
- 23 July 2003

One of the difficulties encountered when studying physical theories in discrete space–time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the… Expand

Symmetry-adapted moving mesh schemes for the nonlinear Schrodinger equation

- C. Budd, V. Dorodnitsyn
- Mathematics
- 23 November 2001

In this paper we consider symmetry-preserving difference schemes for the nonlinear Schrodinger equation where n is the number of space dimensions. This equation describes one-dimensional waves in n… Expand

Finite Difference Models Entirely Inheriting Continuous Symmetry Of Original Differential Equations

- V. Dorodnitsyn
- Mathematics
- 1 August 1994

The present paper is concerned with continuous groups of transformations in a space of discrete variables. The criterion of invariance of difference equations together with difference grid is… Expand

A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures

- V. Galaktionov, V. Dorodnitsyn, G. G. Elenin, S. Kurdyumov, A. A. Samarskii
- Mathematics
- 1 June 1988

A survey is given of results of investigating unbounded solutions (regimes with peaking) of quasilinear parabolic equations of nonlinear heat conduction with a source. Principal attention is devoted… Expand

Transformation groups in net spaces

- V. Dorodnitsyn
- Mathematics
- 1 June 1991

We consider formal groups of transformations on the space of differential and net (finite-difference) variables. We show that preservation of meaning of difference derivatives under transformations… Expand

Symmetry-preserving difference schemes for some heat transfer equations

- M. Bakirova, V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 7 December 1997

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic… Expand

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