  The general PDE governing linear, adiabatic, nonraradial oscillations in a
spherical, differentially and slowly rotating non-magnetic star is derived.
This equation describes mainly low-frequency and high-degree g-modes,
convective g-modes, and rotational Rossby-like vorticity modes and their mutual
interaction for arbitrarily given radial and latitudinal gradients of the
rotation rate. In "traditional approximation" the angular parts of the
eigenfunctions are described by Laplace's tidal equation generalized here to
take into account differential rotation. From a qualitative analysis of
Laplace's tidal equation the sufficient condition for the formation of the
dynamic shear latitudinal Kelvin-Helmholtz instability (LKHI) is obtained. The
exact solutions of Laplace's equation for low frequencies and rigid rotation
are obtained. There exists only a retrograde wave spectrum in this ideal case.
The modes are subdivided into two branches: fast and slow modes. The long fast
waves carry energy opposite to the rotation direction, while the shorter
slow-mode group velocity is in the azimuthal plane along the direction of
rotation. The eigenfuncions are expressed by Jacobi's polynomials which are
polynomials of higher order than the Legendre's for spherical harmonics. The
solar 22-year mode spectrum is calculated. It is shown that the slow 22-year
modes are concentrated around the equator, while the fast modes are around the
poles. The band of latitude where the mode energy is concentrated is narrow,
and the spatial place of these band depends on the wave numbers (l, m).
