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Symmetries of Partial Differential Equations

Conservation Laws — Applications — Algorithms

  • Book
  • © 1989

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Editors:
  1. A. M. Vinogradov

    1. Moscow State University, USSR

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-2
    Download chapter PDF

  2. Part I

    1. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results

      • A. M. Vinogradov
      Pages 3-21

    2. Symmetries and Conservation Laws of Kadomtsev—Pogutse Equations

      • V. N. Gusyatnikova, A. V. Samokhin, V. S. Titov, A. M. Vinogradov, V. A. Yumaguzhin
      Pages 23-64

    3. Symmetries and Conservation Laws of Navier—Stokes Equations

      • V. N. Gusyatnikova, V. A. Yumaguzhin
      Pages 65-81

    4. Symmetries, Invariant Solutions and Conservation Laws of the Nonlinear Acoustics Equation

      • N. O. Sharomet
      Pages 83-120

    5. Local Nonintegrability of Long—Short Wave Interaction Equations

      • A. M. Verbovetsky
      Pages 121-136

    6. On Symmetries and Conservation Laws of the Equations of Shallow Water with an Axisymmetric Profile of Bottom

      • V. S. Titov
      Pages 137-147

    7. On Symmetries of the Heat Equation

      • Yu. R. Romanovsky
      Pages 149-160

    8. Nonlocal Trends in the Geometry of Differential Equations: Symmetries, Conservation Laws, and Bäcklund Transformations

      • I. S. Krasil’shchik, A. M. Vinogradov
      Pages 161-209
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Keywords

About this book

2 The authors of these issues involve not only mathematicians, but also speci­ alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) 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. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.

Editors and Affiliations

  • Moscow State University, USSR

    A. M. Vinogradov

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