  We show that spectral walls are common phenomena in the dynamics of kinks in
(1+1) dimensions. They occur in models based on two or more scalar fields with
a nonempty Bogomol'nyi-Prasam-Sommerfield (BPS) sector, hosting two zero modes,
where they are one of the main factors governing the soliton dynamics. We also
show that spectral walls appear as singularities of the dynamical vibrational
moduli space.
