Small-time expansion of wave motion generated by a submerged sphere

A nonlinear problem of motion of a solid sphere near a free surface of an infinitely deep fluid is considered. For the case of motion with a constant acceleration starting from rest, the solution is studied using a small-time expansion. Expansion coefficients up to the fourth power inclusive are found for the free surface elevation and for the force acting on the sphere. The solutions for linear and nonlinear conditions on the free surface are compared.