  We have proposed a new method for solving the problem of ship waves excited
on the surface of a non-viscous liquid by a submerged object that moves at a
variable speed. As a first application of this method, we have obtained a new
solution to the classic problem of ship waves generated by a submerged ball
that moves rectilinearly with constant velocity parallel to the equilibrium
surface of the liquid. For this example, we have derived asymptotic expressions
describing the vertical displacement of the liquid surface in the limit of
small and large values of the Froude number. The exact solution is presented in
the form of two terms, each of which is reduced to one-dimensional integrals.
One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As
a second example, we considered vertical oscillation of the submerged ball. In
this case, the solution leads to the calculation of one-dimensional integral
and describes surface waves propagating from the epicenter above the ball.
