Influence of Dzialoshinskii-Moriya interaction on static and dynamic properties of a transverse domain wall

It is shown that the Dzialoshinskii-Moriya interaction leads to asymmetrical deformation of the transverse domain wall profile in one-dimensional biaxial magnet. Amplitude of the deformation is linear with respect to the Dzialoshinskii constant $D$. Corrections caused by the Dzialoshinskii-Moriya interaction are obtained for the number of the domain wall parameters: energy density, Doering mass, Walker field. The modified $q$-$\mathrm{\Phi }$ model with an additional pair of conjugated collective variables is proposed for studying the dynamical properties of the wall with taking into account the internal degrees of freedom.