Some properties of the (ψψ)2 model in two dimensions

We show that the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model is, for N = 3, equivalent to the supersymmetric sine-Gordon equation, and for N = 4, equivalent to two decoupled sine-Gordon systems. In addition, we argue that the kinks of this model are isospinors, and we construct some of the higher conservation laws that are responsible for the exact solubility of this system.