Journal of Soviet Mathematics

, Volume 46, Issue 1, pp 1609–1612

Connection between the Kadomtsev-Petviashvili and Johnson equations

  • V. D. Lipovskii
  • V. B. Matveev
  • A. O. Smirnov
Article
  • 33 Downloads

Abstract

The equivalence of the Kadomtsev-Petviashvili and Johnson equations is established in the class of rapidly decreasing Cauchy data. As an illustration of the isomorphism cited the Hamiltonian structure of the Johnson equation is studied.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    S. V. Manakov, Physica D,3, Nos. 1, 2, 420–427 (1981).Google Scholar
  2. 2.
    A. S. Fokas and M. J. Ablowitz, Phys. Lett. A,94, No. 2, 67–70 (1983).Google Scholar
  3. 3.
    M. J. Ablowitz, D. Bar Yaakov, and A. S. Fokas, Stud. Appl. Math.,62, 135–143 (1983).Google Scholar
  4. 4.
    R. E. Johnson, J. Fluid Mech.,97, Pt. 4, 701–719 (1980).Google Scholar
  5. 5.
    V. D. Lipovskii, Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana,21, No. 8, 864–871 (1985).Google Scholar
  6. 6.
    M. A. Sall', “Method of Darboux transformations in the theory of solitons,” Author's Abstract of Candidate's Dissertation, Leningrad State Univ. (1983).Google Scholar
  7. 7.
    V. S. Dryuma, Dokl. Akad. Nauk SSSR,268, No. 1, 15–17 (1983).Google Scholar
  8. 8.
    V. D. Lipovskii, Dokl. Akad. Nauk SSSR,286, No. 2, 334–338 (1986).Google Scholar
  9. 9.
    L. A. Bordag, A. R. Its, S. V. Manakov, V. B. Matveev, and V. E. Zakharov, Phys. Lett. A,63, No. 3, 205–206 (1977).Google Scholar
  10. 10.
    V. B. Matveev, Lett. Math. Phys.,3, 213–216 (1979).Google Scholar
  11. 11.
    V. D. Lipovskii, Vestn. Leningr. Gos. Univ., Ser. Fiz. Khim., No. 2, 73–77 (1986).Google Scholar
  12. 12.
    L. D. Faddeev and L. A. Takhtajan, Lett. Mat. Phys.,10, No. 4, 183–188 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • V. D. Lipovskii
  • V. B. Matveev
  • A. O. Smirnov

There are no affiliations available

Personalised recommendations