  A general equation describing the resonant nonlinear mode-coupling among
kinetic Alfv\'en waves (KAWs) is derived using nonlinear gyrokinetic theory,
which can be applied to study the potentially strong spectral energy transfer
of KAWs. As a first application, the parametric decay of a pump KAW into two
sideband KAWs are studied, with particular emphasis on the cascading in
perpendicular wavenumber. It is found that, for the "co-propagating" cases with
all three KAWs propagating in the same direction along the equilibrium magnetic
field line, it exhibits a dual cascading character in the perpendicular
wavenumber space; while for the "counter-propagating" cases with one sideband
propagating in the opposite direction with respect to the pump wave, it
instead, can exhibit both dual and inverse cascading behaviors. The
implications on SAW instability nonlinear saturation and charged particle
transport in fusion plasmas is also discussed.
