Bridging the Dimensional Gap: from Kink in One Dimension to Curved Domain Wall in Three Dimensions

Improved expansion in width is applied to a curved domain wall in nonrelativistic dissipative $\lambda ({\mathrm{\Phi }}^2-v^2{)}^2$ model with real scalar order parameter $\mathrm{\Phi }$. Approximate analytic description of such a domain wall to second order in the width is presented.