Skip to main content
SpringerLink
Log in

Computer algebra application for investigating integrability of nonlinear evolution systems

  • Applications And Systems
  • Conference paper
  • First Online:
Book cover Eurocal '87 (EUROCAL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 378))

Included in the following conference series:

  • 159 Accesses

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zhiber A.V., Shabat A.B. (1979). Klein-Gordon equation with nontrivial group. DNA SSSR 247, 1103 (in Russian).

    Google Scholar 

  2. Svinolupov S.I., Sokolov V.V. (1982). On the evolution equations with nontrivial conservation laws. Funct. Anal. 16,86 (in Russian).

    Google Scholar 

  3. Svinolupov S.I. (1985). Second order evolution equations possesing metries. Usp. Mat. Nauk 40,263 (in Russian).

    Google Scholar 

  4. Mikhailov A.V., Shabat A.B. (1985). Integrability conditions for system of two equations of form u t=A(u)u xx+F(u,u x ) I. Theor. &Math.Phys. 62,163 (in Russian).

    Google Scholar 

  5. Mikhailov A.V., Shabat A.B. (1986). Integrability conditions for system of two equations of form u t=A(u)u xx+F(u,u x ) II. Theor.& Math. Phys. 66, 47 (in Russian).

    Google Scholar 

  6. Shabat A.B., Yamilov R.I. (1985). On complete list of integrable equations of form: iu t=u xx+f(u,v,u x,v x ),-iv t=v xx+g(u,v,u x,v x ). Preprint BF AN SSSR, Ufa (in Russian).

    Google Scholar 

  7. Ibragimov N.H., Shabat A.B. (1984). On infinite Lie-Bäcklund algebras. Funct. Anal. 14,79 (in Russian).

    Google Scholar 

  8. Fokas A.S. (1987). Symmetries and integrability. Stud. Appl. Math. 77,253.

    Google Scholar 

  9. Sokolov V.V., Shabat A.B. (1984). Classification of integrable evolution equations. Math. Phys. Rev. 4,221, New York.

    Google Scholar 

  10. Mikhailov A.V., Shabat A.B., Yamilov R.I. (1987). Symmetry approach to classification of nonlinear equations. Complete list of integrable systems. Usp. Mah. Nauk 42,3 (in Russian).

    Google Scholar 

  11. Buchberger B., Collins G.E., Loos R. (eds.) (1983). Computer algebra: symbolic and algebraic computation, 2nd edition, Vienna: Springer-Verlag.

    Google Scholar 

  12. Zharkov A.Yu., Shvachka A.B. (1983). REDUCE-2 program for investigating integrability of nonlinear evolution equations. Preprint JINR, R11-83-914, Dubna (in Russian).

    Google Scholar 

  13. Gerdt V.P., Shvachka A.B., Zharkov A.Yu. (1985). FORMINT-a program for classification of integrable nonlinear evolution equations. Comp. Phys. Comm. 34,303.

    Article  Google Scholar 

  14. Gerdt V.P., Shvachka A.B., Zharkov A.Yu. (1985). Computer algebra application for classification of integrable nonlinear evolution equations. J. Symb. Comp. 1, 101.

    Google Scholar 

  15. Zakharov V.E., Manakov S.V., Novikov S.P., Pitaevsky L.P. (1980). Theory of solitons. The inverse problem method, Moscow, Nauka (in Russian).

    Google Scholar 

  16. Gelfand I.M., Manin Yu.I., Shubin M.A. (1976). Pouasson brackets and nel of variational derivative in formal variational calculus. Funct. Anal. 10,30 (in Russian).

    Google Scholar 

  17. Bahr K.A. (1973). FORMAC 73 user's manual, Darmstadt: GMD/IFV.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Head Post Office, P.O. Box 79, Moscow, USSR

    V. P. Gerdt

  2. Bashkir Branch of the USSR Academy of Sciences, Ufa, USSR

    A. B. Shabat & S. I. Svinolupov

  3. Saratov State University, Astrakhanskaya 83, Saratov, USSR

    A.Yu. Zharkov

Authors
  1. V. P. Gerdt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Shabat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. I. Svinolupov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A.Yu. Zharkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

James H. Davenport

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gerdt, V.P., Shabat, A.B., Svinolupov, S.I., Zharkov, A. (1989). Computer algebra application for investigating integrability of nonlinear evolution systems. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_92

Download citation

  • DOI: https://doi.org/10.1007/3-540-51517-8_92

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51517-3

  • Online ISBN: 978-3-540-48207-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation