Curved, extended classical solutions I. The undulating kink

TL;DR

This paper investigates the curvature energy of kinks in two-dimensional classical solutions, revealing it to be always negative and providing a closed-form expression for small deviations from straightness.

Contribution

It introduces a novel analytical expression for the curvature energy of kinks, highlighting its negative nature in two dimensions.

Findings

Curvature energy of kinks is always negative.

Derived a closed-form expression for small deviations.

Implications for the stability of extended classical objects.

Abstract

The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We obtain a closed form for the curvature energy, assuming small deviations from the straight line.