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This paper examines the effects of a thin layer of inhomogeneity on periodicsolutions of the Multiple-sine-Gordon (MsG) model. We investigate the dynamicsof the perturbed Double-sine-Gordon (DsG) system as a significant and morepractical case of such configurations. The thin barrier acts as a potentialwell (potential barrier) and causes critical deformations in kink trainsolutions and some basic properties of the periodic solutions, such as the typeof sub-kinks, their amplitude, energy and wavelength. Stability of the initialkink chain during the interaction with medium defects is analyzed using theirphase diagram. Sudden changes in the profile of kink trains due to thedisruption of their amplitude and wavelength are considered. The time evolutionof moving kink chain solutions while interacting with medium fractures is alsostudied.

Dynamics of kink train solutions in deformed Multiple sine-Gordon models