Oscillating kink behavior in a traversable wormhole

We investigate the time evolution of spherically symmetric radial domain walls (kinks) in the background of a two-way traversable Simpson-Visser wormhole. By numerically solving the scalar-field equation with a double-well potential, we show that the wormhole throat parameter $a$ has a strong impact on the dynamics of the radial kink: larger $a$ leads to wider throats and allows the domain wall to oscillate across the throat with large amplitude, whereas smaller $a$ confines the motion nearby the throat. In addition, each time the kink crosses the wormhole throat, it emits scalar wave packets, causing its oscillation amplitude to gradually decrease. Our results reveal how the wormhole geometry influences the motion of defects and their energy transfer, providing new insights into the dynamics of topological defects in exotic spacetime.