  The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly
anisotropic and dispersive plasmas, developed for slow resonance by Clack and
Ballai [Phys. Plasmas, 15, 2310 (2008)] and Alfv\'en resonance by Clack
\emph{et al.} [A&A,494, 317 (2009)], is used to study the weakly nonlinear
interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar
plasma. The magnetic configuration consists of an inhomogeneous magnetic slab
sandwiched between two regions of semi-infinite homogeneous magnetic plasmas.
Laterally driven FMA waves penetrate the inhomogeneous slab interacting with
the localized slow or Alfv\'{e}n dissipative layer and are partly reflected,
dissipated and transmitted by this region. The nonlinearity parameter defined
by Clack and Ballai (2008) is assumed to be small and a regular perturbation
method is used to obtain analytical solutions in the slow dissipative layer.
The effect of dispersion in the slow dissipative layer is to further decrease
the coefficient of energy absorption, compared to its standard weakly nonlinear
counterpart, and the generation of higher harmonics in the outgoing wave in
addition to the fundamental one. The absorption of external drivers at the
Alfv\'{e}n resonance is described within the linear MHD with great accuracy.
