Sine-Gordon Solitons

Kink–antikink scattering — topological field theory in 1+1 dimensions

Simulation

Theory

∂²φ/∂t² − ∂²φ/∂x² + sin(φ) = 0

Kink solution:
φ(x,t) = 4 arctan(exp(γ(x−vt)))

γ = 1/√(1−v²) (Lorentz factor)

Topological charge:
Q = (φ(+∞)−φ(−∞))/2π = ±1

Energy: M = 8γ (relativistic mass)
Q_total: --
E_kink: --
E_total: --
Phase: --