φ⁴ field theory kinks: topological defects that cannot be removed by continuous deformations. Watch kink-antikink collisions — they can annihilate or form breathers depending on velocity.
The φ⁴ kink φ(x,t) = tanh((x-vt)/√(1-v²)·√2) connects two vacuum states φ=±1. Topological charge Q=±1 is conserved — kinks cannot be created or destroyed singly. Kink-antikink scattering shows fractal resonance windows (Anninos et al. 1991). Sine-Gordon solitons scatter elastically.