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Summation of the Witting series in the solitary wave problem

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References

  1. L. V. Ovsyannikov, “On the asymptotic representation of solitary waves,” Dokl. Akad. Nauk SSSR,318, No. 3, 556–559 (1991).

    Google Scholar 

  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. K. O. Friedrichs and D. H. Hyers, “The existence of solitary waves,” Comm. Pure Appl. Math.,7, 517–550 (1954).

    Google Scholar 

  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. 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. J. Witting, “On the highest and other solitary waves,” J. Appl. Math.,28, No. 3, 700–719 (1975).

    Google Scholar 

  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. S. A. Pennell, “On a series expansion for the solitary wave,” J. Fluid Mech.,179, 557–561 (1987).

    Google Scholar 

  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. J. K. Hunter and J. M. Vanden-Broeck, “Accurate computations for steep solitary waves,” J. Fluid Mech.,136, 63–71 (1983).

    Google Scholar 

  11. J. Witting, “High solitary waves in water: results of calculations,” NRL Rep., 1981, No. 8505.

  12. M. van Dyke, “Semi-analytical applications of the computer,” Fluid Dynamics Transl. Warszawa,9, 305–320 (1978).

    Google Scholar 

  13. G. A. Baker and P. Graves-Morris, Padé Approximations [Russian translation], Mir, Moscow (1986).

    Google Scholar 

  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. K. I. Babenko, Fundamentals of Numerical Analysis [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  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 

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Translated from Sibirskiĩ Matematicheskiĩ, Vol. 36, No. 2, pp. 328–347, March–April, 1995.

The author expresses gratitude to Academician L. V. Ovsyannikov who posed the problem and evinced interest in the article.

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Karabut, E.A. Summation of the Witting series in the solitary wave problem. Sib Math J 36, 287–304 (1995). https://doi.org/10.1007/BF02110150

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