  We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein
condensate periodically driven by a quadratic Zeeman coupling. This phenomenon
is closely related to the Shapiro steps in superconducting Josephson junctions,
and the previous experimental work [Evrard $et al.,$ Phys. Rev. A 100, 023604
(2019)] for a spin-1 bosonic system observed the resonant dynamics and then
called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii
equation, we study the Shapiro resonance beyond the single-mode approximation
used in the previous work, which assumes that all components of the spinor
wavefunction have the same spatial configuration. Considering resonant dynamics
starting from a polar state, we analytically calculate the Floquet-Lyapunov
exponents featuring an onset of the resonance under a linear analysis and find
that spin waves with finite wavenumbers can be excited. This kind of
non-uniform excitation cannot be described by the single-mode approximation.
Furthermore, to study the long-time resonant dynamics beyond the linear
analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii
equation, finding that the nonresonant hydrodynamic variables also grow at
wavelengths of even multiples of the resonant one due to the nonlinear effect.
