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Barchans are crescent-shaped dunes found in deserts with little sand, where winds blow continuously in one direction. They migrate in the downwind direction at speeds of several meters per year as sand eroded from the upwind slope is deposited on the downwind side. A characteristic feature of barchans is the localized sand outflow from their downwind-extending horns. Because barchans typically exist in clusters, this horn outflow can become sand inflow to barchans located further downwind, inducing sand-mediated interaction between upwind and downwind barchans.Most previous studies on barchan interaction have focused on direct contact interactions, i.e., collisions. However, it has recently been recognized that non-contact interaction mediated by sand transport can occur without collision. Studies on this type of interaction remain limited.This research focuses on non-contact sand-mediated interaction between upwind and downwind barchans. The interaction is investigated using a simplified crest line model [1]. This model is characterized by a small number of variables, which provides a distinct advantage in making theoretical analysis tractable.We obtain an analytical steady-state solution. The steady-state barchan shape is symmetric with respect to the sand supply source. The steady-state configuration consists of two parabolic solutions whose axes are laterally shifted due to sand inflow and connected at the supply source. Both the crest height of the steady-state barchan and the lateral displacement of the axes can be obtained analytically. We find that the steady-state barchan shape is determined by the migration velocity of the barchan and the sand inflow rate. In addition, the inverse proportionality between barchan height and migration velocity is theoretically confirmed in this study, a relationship well known in previous studies.The analytical solution shows good agreement with our previous numerical results. Our results provide deeper mathematical insight into non-contact sand-mediated interaction in barchan dune fields and offer a foundation for future studies on barchan collisions.[1] L. Guignier. et al., Sand dunes as migrating strings, Physical Review E (2013)