  The interaction between transverse magnetic domain walls (TDWs) in planar
(2D) and cylindrical (3D) nanowires is examined using micromagnetic
simulations. We show that in perfect and surface deformed wires the free TDWs
behave differently, as the 3D TDWs combine into metastable states with average
lifetimes of 300ns depending on roughness, while the 2D TDWs do not due to 2D
shape anisotropy. When the 2D and 3D TDWs are pinned at artificial
constrictions, they behave similarly as they interact mainly through the
dipolar field. This magnetostatic interaction is well described by the point
charge model with multipole expansion. In surface deformed wires with
artificial constrictions, the interaction becomes more complex as the depinning
field decreases and dynamical pinning can lead to local resonances. This can
strongly influence the control of TDWs in DW-based devices.
