Klein-Gordon Soliton Kink

φ-⁴ field theory: ∂²φ/∂t² − ∂²φ/∂x² + φ³ − φ = 0. Kink solution φ = tanh(γ(x−vt)/√2). Watch kink-antikink collision — breather formation vs annihilation.

φ = tanh(γ(x−x₀)/√2)
γ = 1/√(1−v²)
Energy = ∫[(∂φ/∂t)²/2 + (∂φ/∂x)²/2 + V(φ)] dx
V(φ) = (1−φ²)²/4
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