Dynamics of a Traveling Kink in a One-Dimensional System with a Quenched Impurity

Abstract

Dynamics of a traveling kink in the presence of a localized quenched impurity is investigated both numerically and analytically for one-dimensional system described by the Nagumo equation without the thermal noise. We find the following results. (i) The interaction between the traveling kink and the impurity is attractive. (ii) If the impurity effect is weak, the traveling kink passes through the impurity position and the phase shift of the trajectory of the kink position from that of the unperturbed motion takes a positive or negative value depending on both the impurity effect and the velocity of unperturbed motion. (iii) If the impurity effect is strong, the traveling kink is pinned by the impurity position. (iv) When the distance between the traveling kink and the impurity is large, a spiky defect is formed in the order parameter profile at the impurity position.