Advertisement

Siberian Mathematical Journal

, Volume 36, Issue 2, pp 287–304 | Cite as

Summation of the Witting series in the solitary wave problem

  • E. A. Karabut
Article

Keywords

Solitary Wave Wave Problem Witting Series Solitary Wave Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. V. Ovsyannikov, “On the asymptotic representation of solitary waves,” Dokl. Akad. Nauk SSSR,318, No. 3, 556–559 (1991).Google Scholar
  2. 2.
    M. A. Lavrent'ev, “To the theory of long waves,” in: Selected Works. Mathematics and Mechanics [in Russian], Nauka, Moscow, 1990, pp. 524–570.Google Scholar
  3. 3.
    K. O. Friedrichs and D. H. Hyers, “The existence of solitary waves,” Comm. Pure Appl. Math.,7, 517–550 (1954).Google Scholar
  4. 4.
    M. S. Longuet-Higgins and J. D. Fenton, “On the mass, momentum, energy, and circulation of a solitary wave. II,” Proc. Roy. Soc. London Ser. A,340, 471–493 (1974).Google Scholar
  5. 5.
    P. I. Plotnikov, “Nonuniqueness of a solution to the solitary wave problem and bifurcation of critical points for smooth functionals,” Izv. Akad. Nauk SSSR Ser. Mat.,55, No. 2, 339–366 (1991).Google Scholar
  6. 6.
    J. Witting, “On the highest and other solitary waves,” J. Appl. Math.,28, No. 3, 700–719 (1975).Google Scholar
  7. 7.
    S. A. Pennell and C. H. Su, “A seventeenth-order series expansion for the solitary wave,” J. Fluid Mech.,149, 431–443 (1984).Google Scholar
  8. 8.
    S. A. Pennell, “On a series expansion for the solitary wave,” J. Fluid Mech.,179, 557–561 (1987).Google Scholar
  9. 9.
    J. M. Williams, “Limiting gravity waves in water of finite depth,” Philos. Trans. Roy. Soc. London Ser. A,302, 139–188 (1981).Google Scholar
  10. 10.
    J. K. Hunter and J. M. Vanden-Broeck, “Accurate computations for steep solitary waves,” J. Fluid Mech.,136, 63–71 (1983).Google Scholar
  11. 11.
    J. Witting, “High solitary waves in water: results of calculations,” NRL Rep., 1981, No. 8505.Google Scholar
  12. 12.
    M. van Dyke, “Semi-analytical applications of the computer,” Fluid Dynamics Transl. Warszawa,9, 305–320 (1978).Google Scholar
  13. 13.
    G. A. Baker and P. Graves-Morris, Padé Approximations [Russian translation], Mir, Moscow (1986).Google Scholar
  14. 14.
    E. A. Karabut, “An application of power series in time to the problem of motion of a cylindrical cavity in a fluid. II. Determination of singular points,” Dinamika Sploshn. Sredy (Novosibirsk),80, 63–81 (1987).Google Scholar
  15. 15.
    K. I. Babenko, Fundamentals of Numerical Analysis [in Russian], Nauka, Moscow (1986).Google Scholar
  16. 16.
    M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • E. A. Karabut
    • 1
  1. 1.Novosibirsk

Personalised recommendations