  In this paper, we present a new approach for solving Laplace tidal equations
(LTE) which was formulated first in [S.V.Ershkov, A Riccati-type solution of
Euler-Poisson equations of rigid body rotation over the fixed point, Acta
Mechanica, 228(7), 2719 (2017)] for solving Poisson equations: a new type of
the solving procedure for Euler-Poisson equations (rigid body rotation over the
fixed point) is implemented here for solving momentum equation of LTE, Laplace
tidal equations. Meanwhile, the system of Laplace tidal equations (including
continuity equation) has been successfully explored with respect to the
existence of analytical way for presentation of the solution. As the main
result, the new ansatz is suggested here for solving LTE: solving momentum
equation is reduced to solving system of 3 nonlinear ordinary differential
equations of 1-st order in regard to 3 components of the flow velocity
(depending on time t), along with the continuity equation which determines the
spatial part of solution. Nevertheless, the proper elegant partial solution has
been obtained due to invariant dependence between temporary components of the
solution. In addition to this, it is proved here that the system of Laplace
tidal equations has not the analytical presentation of solution (in
quadratures) in case of nonzero fluid pressure in the Ocean, as well as nonzero
total gravitational potential and the centrifugal potential (due to planetary
rotation).
