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Summation of the Witting series in the solitary wave problem. (English. Russian original) Zbl 0861.76009
Sib. Math. J. 36, No. 2, 287-304 (1995); translation from Sib. Mat. Zh. 36, No. 2, 328-347 (1995).
A series \(\sum E_j \exp (jz)\), \(\text{Im} E_j =0\), of the complex variable \(z\) is analyzed for constructing a solitary wave for a two-dimensional vortex-free stationary flow of an ideal incompressible heavy fluid over a flat bottom. Summation of the series is reduced to solution of a system of ordinary differential equations. It is shown that the solutions do not describe solitary waves but they are very close to them.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
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