Soliton Kinks — Sine-Gordon Equation

The sine-Gordon equation ∂²φ/∂t² − ∂²φ/∂x² + sin(φ) = 0 supports topological solitons (kinks and antikinks). Kinks collide elastically, emerging unchanged — a hallmark of integrable field theory.

Kink 1

Kink 2

Setup

Running…
φ(x,t) shown as field height
Color = topological charge density