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

TL;DR

This paper develops an improved analytical method to describe curved domain walls in a nonrelativistic dissipative scalar field model, extending understanding from one-dimensional kinks to three-dimensional curved structures.

Contribution

It introduces a second-order approximate analytic description of curved domain walls in a dissipative scalar field model, bridging the gap from one-dimensional kinks to three-dimensional walls.

Findings

Analytic description of curved domain walls to second order in width.

Extension of kink solutions from one dimension to curved three-dimensional structures.

Enhanced understanding of domain wall behavior in dissipative scalar field models.

Abstract

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