This study provides new insights into the nature of seasonal variations in coordinate time series of GPS sites located near active faults and methods of their modeling. Monthly averaged coordinate time series were analyzed for several pairs of collocated GPS sites situated near the active fault intersection area, in close proximity to the central part of the northern boundary of the Amurian plate and the vicinity of the San Andreas Fault zone. It is concluded that the observed seasonal variations are best described by a breather function which is one of the solutions of the well-known sine-Gordon equation. The obtained results suggest that, in this case, the source of seasonal variations may be caused by the appearance of solitary strain waves in the fault intersection system, which may be qualitatively treated as standing waves of compression-extension of the geological medium. Based on statistical testing, the limits of applicability of the suggested model have been established.