The fully nonlinear problem on the unsteady water waves generated by submerged moving cylinder is considered. Using the analytic majorant method we prove local in time unique solvability of this problem. For the case when the dimensionless cylinder radius is small, the solution estimate obtained predicts rigorously dipole-like structure for the lowest order far field flow. The strength of dipole concentrated at the cylinder axis depends on the instantaneous wave form and fluid velocity at the free surface. Special case of the lifting accelerated cylinder starting from the rest is studied analytically in more detail.

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