is equivalent to the sine-Gordon equation φ φ u v = sin ⁡ ⁡ φ φ . The zero-curvature equation is so named as it corresponds to the curvature being equal to zero if it is defined F μ μ ν ν = [ ∂ ∂ μ μ − − A μ μ , ∂ ∂ ν ν − − A ν ν ] .