We study the propagation of solitary waves of vortices within a spheri
cal shell which constitutes the uppermost layer of a solid planet. Thi
s solid-liquid configuration rotates with constant angular velocity ab
out an axis which is fixed with respect to the solid surface. The flui
d within the shell is inviscid, incompressible, and of constant densit
y. The motion imparted by the planetary rotation upon this fluid mass
is governed by the Laplace tidal equation from which the potential of
the extraplanetary forces has been deleted. Consistent with this ocean
model, we establish that the stream function of a solitary wave of vo
rtices must satisfy a third-order partial differential equation. We ob
tain solutions to this wave equation by imposing the condition that th
e vertical component of vorticity be functionally related to the strea
m function. We find that this dependence must necessarily be of the ex
ponential type and that the solution to the wave equation then reduces
to a quadrature depending on some arbitrary parameters. We prove that
we can always choose the values of these parameters in order to appro
ximate the integral in question by means of an analytic function: we r
each a representation of the stream function of a solitary wave of vor
tices in terms of hyperbolic functions of time and position.