  Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous,
weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive
plasma is investigated. 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 localised slow or Alfven waves present in the
inhomogeneous layer and are partly reflected, dissipated and transmitted by
this region. The presented research aims to find the coefficient of wave energy
absorption under solar chromospheric and coronal conditions. Numerical results
are analyzed to find the coefficient of wave energy absorption at both the slow
and Alfven resonance positions. The mathematical derivations are based on the
two simplifying assumptions that (i) nonlinearity is weak, and (ii) the
thickness of the inhomogeneous layer is small in comparison to the wavelength
of the wave, i.e. we employ the so-called long wavelength approximation. Slow
resonance is found to be described by the nonlinear theory, while the dynamics
at the Alfven resonance can be described within the linear framework. We
introduce a new concept of coupled resonances, which occurs when two different
resonances are in close proximity to each other, causing the incoming wave to
act as though it has been influenced by the two resonances simultaneously. Our
results show that the wave energy absorption is heavily dependent on the angle
of the incident wave in combination with the inclination angle of the
equilibrium magnetic field. In addition, it is found that FMA waves are very
efficiently absorbed at the Alfven resonance under coronal conditions. Under
chromospheric conditions the FMA waves are far less efficiently absorbed,
despite an increase in efficiency due to the coupled resonances.
