Abstract
The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
VinogradovA. M.: A spectral sequence associated with a nonlinear differential equation and algebra-geometric foundations of Lagrangian field theory with constraints,Dokl. Acad. Nauk. SSSR 238 (1978), 1028–1031 (English translation inSoviet Math. Dokl. 19 (1978), 144–148).
VinogradovA. M.: The theory of higher infinitesimal symmetries of nonlinear partial differential equations,Dokl. Acad. Nauk. SSSR 248 (1979), 274–278 (English translation inSoviet Math. Dokl. 20 (1979), 985–990).
VinogradovA. M. Local symmetries and conservation laws,Acta Appl. Math. 2 (1984), 21–78.
VinogradovA. M.: TheC-spectral sequence, Lagrangian formalism and conservation laws,J. Math. Anal. Appl. 100 (1984), 2–129.
IbragimovN. H.:Transformation Groups Applied to Mathematical Physics, D. Reidel, Dordrecht, 1985.
OliverP. J.:Application of Lie Groups to Differential Equations, Springer, New York, 1986.
GusyatnikovaV. N., SamokhinA. V., TitovV. S., VinogradovA. M., and YumaguzhinV. A.: Symmetries and conservation laws Kadomtsev-Pogutse equations,Acta Appl. Math. 15 (1989), 23–64.
GusyatnikovaV. N. and YumaguzhinV. A.: Symmetries and conservation laws of Navier-Stokes equations,Acta Appl. Math. 15 (1989), 65–81.
TitovV. S.: On symmetries and conservation laws of the equations of shallow water with an axisymmetric profile of bottom,Acta Appl. Math. 15 (1989), 137–147.
VerbovetskyA. M.: Local nonintegrability of the long-short wave interaction equations,Acta Appl. Math. 15 (1989), 121–136.
SharometN. O.: Symmetries, invariant solutions and conservation laws of the nonlinear acoustics equation,Acta Appl. Math 15 (1989), 83–120.
RomanovskyYu. R.: On symmetries of the heat equation,Acta Appl. Math. 15 (1989), 149–160.
Krasil'shchikI. S., LychaginV. V., and VinogradovA. M.:Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach, New York, 1986.
SenashovS. I. and VinogradovA. M.: Symmetries and conservation laws of 2-dimensional ideal plasticity.Proc. Edinburgh Math. Soc. 31 (1988), 415–439.
Krasil'shchikI. S. and VinogradovA. M.: Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations,Acta Appl. Math. 15 (1989), 161–209.
GusyatnikovaV. N., VinogradovA. M., and YumaguzhinW. A.: Secondary differential operators,J. Geom. Phys. 2 (1985), 23–66.
TsujishitaT.: On variation biocomplexes associated to differential equations,Osaka Math. J. 19 (1982), 311–363.
AstashovA. M. and VinogradovA. M.: On the structure of Hamiltonian operators in field theory.J. Geom. Phys. 3 (1986), 264–287.
Vinogradov, A. M.: The category of differential equations and its significance for physics,Proc. Conf. Differential Geometry and its Applications. Nove Mesto na Morave (VSSR), 5–9 September 1983, Part 2, pp. 289–301.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vinogradov, A.M. Symmetries and conservation laws of partial differential equations: Basic notions and results. Acta Appl Math 15, 3–21 (1989). https://doi.org/10.1007/BF00131928
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00131928