a nanostrip or in a bubble domain, an easy-axis field $H_{z}$ drives the DW dynamics in the presence of an in-plane field $H_{x}$ (aligned along $+x$), the DW speed is different for up/down and down/up DDWs propagating along $\pm x$ [@Je2013; @Hrabec2014; @Jue2015]. This phenomenon is related to the symmetry breaking introduced by the in-plane field. The Dzyaloshinskii-Moriya interaction acts as a longitudinal chiral field $H_{\mathrm{DMI}}=D/(\mu_{0}M_{s}\Delta)$ (where $D$ is the DMI strength, $M_{s}$ is the saturation magnetisation and $\Delta$ is the domain wall width parameter) localised on the domain walls, having opposite directions for up/down and down/up DWs. Beyond a critical strength, the DMI forces the DW magnetisation in the Néel configuration (see sketch in Figure \[fig:images\]) [@Thiaville2012]. Although the in-plane field does not drive the dynamics, it will respectively stabilise (*vs.* destabilise) the DWs having their magnetisation $m$ parallel (*vs.* antiparallel) to it. For a parallel (*vs.* antiparallel) alignment between $H_{x}$ and $m$ the DW speed increases (*vs.* decreases) with respect to the $H_{x}$=0 case. In the high speed (flow) regime, the speed increase (vs. decrease) is mainly due to the widening (vs. narrowing) of the DW with $H_{x}$ [@Jue2015]. In the low speed (thermally-activated or creep) regime, the 