Summation of the Witting series in the solitary wave problem (Q1921780)

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.