Summation of the witting series in the solitary-wave problem

  • E. A. Karabut


Some exact solutions of the Euler equations with a free surface in the presence of gravitation forces are found. They are obtained by summing Witting series applied in the theory of solitary waves. It is shown that in some cases, the left-hand half of the constructed flows is close to the left-hand half of the solitary waves.


Free Surface Solitary Wave Gravitational Wave Conformal Mapping Discrete Fourier Transform 
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  1. 1.
    J. Witting, “On the highest and other solitary waves,”J. Appl. Math. 28, No. 3, 700–719 (1975).MATHGoogle Scholar
  2. 2.
    E. A. Karabut, “The solitary-wave problem on the surface of a fluid,”Dokl. Ross. Akad. Nauk,337, No. 3, 339–341 (1994).MATHMathSciNetGoogle Scholar
  3. 3.
    E. A. Karabut, “Summation of the Witting series in the solitary-wave problem,”Sib. Mat. Zh.,36, No. 2, 328–348 (1995).MATHMathSciNetGoogle Scholar
  4. 4.
    E. A. Karabut, “Asymptotic expansions in the solitary-wave problem,”J. Fluid Mech.,319, 109–123 (1996).MATHMathSciNetCrossRefADSGoogle Scholar
  5. 5.
    E. A. Karabut, “The family of exact solutions close to gravity waves of maximum amplitude,”Dokl. Ross. Akad. Nauk,344, No. 5, 623–626 (1995).MATHMathSciNetGoogle Scholar
  6. 6.
    E. A. Karabut, “Theory of maximum-amplitude gravitational waves,”Vychisl. Tekhnol.,4, No. 11, 127–143 (1995).Google Scholar
  7. 7.
    E. A. Karabut, “An approximation for the highest gravity waves on water of finite depth,”J. Fluid Mech.,372, 45–70 (1998).MATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    L. V. Ovsyannikov, “Asymptotic representation of solitary waves,”Dokl. Akad. Nauk USSR,318, No. 3, 556–559 (1991).MATHMathSciNetGoogle Scholar
  9. 9.
    E. A. Karabut, “Numerical analysis of the asymptotic representation of solitary waves,”Prikl. Mekh. Tekh. Fiz.,35, No. 5, 44–54 (1994).MATHMathSciNetGoogle Scholar
  10. 10.
    K. I. Babenko, “Some remarks on the theory of finite-amplitude surface waves,”Dokl. Akad. Nauk USSR,294, No. 5, 1033–1037 (1987).MATHMathSciNetGoogle Scholar
  11. 11.
    J. B. Keller, “The solitary wave and periodic waves in shallow water,”Commun. Pure Appl. Math.,1, 323–339 (1948).MATHGoogle Scholar
  12. 12.
    S. A. Pennel, “On a series expansion for the solitary wave,”J. Fluid Mech.,179, 557–561 (1987).MathSciNetCrossRefADSGoogle Scholar
  13. 13.
    M. S. Longuet-Higgins, “Some new relations between Stokes's coefficients in the theory of gravity waves,”J. Inst. Math. Appl.,22, No. 3, 261–273 (1977).MathSciNetCrossRefGoogle Scholar

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© Kluwer Academic/Plenum Publishers 1999

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  • E. A. Karabut

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