  In N=4 super Yang-Mills spin chain, we compute reflection amplitudes of
magnon bound-state off giant graviton. We first compute the reflection
amplitude off Y=0 brane boundary and compare it with the scattering amplitude
between two magnon bound-states in the bulk. We find that analytic structure of
the two amplitudes are intimately related each other: the boundary reflection
amplitude is a square-root of the bulk scattering amplitude. Using such
relation as a guide and taking known results at weak and strong coupling limits
as inputs, we find the reflection amplitude of an elementary magnon off Z=0
giant graviton boundary. The reflection phase factor is shown to solve crossing
and unitarity relations. We then compute the reflection amplitude of magnon
bound-state off the Z=0 brane boundary and observe that its analytic structures
are again intimately related to the bulk scattering and the Y=0 boundary
reflection amplitudes. We also take dyonic giant magnon limit of these
reflection amplitudes and confirm that their phase-shifts agree completely with
string worldsheet computations based on complex sine-Gordon soliton scattering.
