The 1-soliton solution for which we have chosen the positive root for γ γ is called a kink and represents a twist in the variable φ φ which takes the system from one constant solution φ φ = 0 to an adjacent constant solution φ φ = 2 π π . The states φ φ ≅ ≅ 2 π π n are known as vacuum states, as they are constant solutions of zero energy. The 1-soliton solution in which we take the negative root for γ γ is called an antikink. The form of the 1-soliton solutions can be obtained through application of a Bäcklund transform to the trivial (vacuum) solution and the integration of the resulting first-order differentials: