Skip to main content
SpringerLink
Log in

On the background of limit pass for Korteweg-de Vries equation as the dispersion vanishes

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

We present the new approach to the background of approximate methods of convergence based on the theory of functional solutions and solutions in the mean one for conservation laws. The applications to the Cauchy problem to KdV equation, when dispersion tends to zero are considered. Also the Galerkin method for a periodic problem for the KdV equation is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Galkin, V. A.: Functional solutions of conservation laws,Doklady Akad. Nauk SSSR 310 (1990), 834–839;English transl, inSov. Phys. Dokl. 35(2) (1990), 133–135.

    Google Scholar 

  2. Galkin, V. A.: inProc. Int. Meeting on Ordinary Diff. Equations and Their Applications, Italy, Florence, Sept. 1993, p. 52.

  3. Galkin, V. A.: Numerical stability and convergence of approximate methods for conservation laws,J. Modern Phys. C (to appear).

  4. Filippov, A. F.: Ordinary differential equations with discontinuity in right-hand side,Mat. Sbornik SSSR 51 (1960), (in Russian).

  5. Galkin, V. A. and Russkikh, V. V.:Proc. Inst. Atomic Energetics 2 (1992).

  6. Galkin, V. A. and Russkikh, V. V.: Convergence of approximate methods for equations of incompressible fluid dynamics,Mathematical Modeling 6 (1994), 101–113 (in Russian).

    Google Scholar 

  7. Galkin, V. A.: Generalized solution of the Smoluchowski kinetic equation for spatially inhomogeneous systems,Sov. Phys. Dokl. 32(3) (1987), 200–201.

    Google Scholar 

  8. Galkin, V. A. and Tupchiev, V. A.: On solvability in the mean of a system of quasilinear conservation laws,DAN SSSR 300 (1988).

  9. Di Perna, R. J.: Measure-value solutions of conservation laws,Arch. Ration. Mech. Anal. 88 (1985), 223–270.

    Google Scholar 

  10. Lax, P. D.: Integrals of nonlinear equations of evolution and solitary waves,Commun. Pure Appl. Math. 21 (1968).

  11. Kadomtzev, B. B.:Collective Phenomena in Plasma, Nauka, Moscow, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Atomic Energetics, 249020, Obninsk, Russia

    V. A. Galkin & V. V. Russkikh

Authors
  1. V. A. Galkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Russkikh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galkin, V.A., Russkikh, V.V. On the background of limit pass for Korteweg-de Vries equation as the dispersion vanishes. Acta Appl Math 39, 307–314 (1995). https://doi.org/10.1007/BF00994639

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00994639

Mathematics subject classification (1991)

Key words

Search

Navigation