Gauge equivalence of differential equations describing surfaces of constant Gaussian curvature (Q2761885)

The authors of this interesting paper generalize the result of \textit{N. Kamran} and \textit{K. Tenenblat} [J. Differ. Equ. 115, 75-98 (1995; Zbl 0815.35036)] to differential equations or systems describing surfaces of constant Gaussian curvature and interprete them geometrically in terms of local gauge transformations. This reveals a quite universal phenomenon that local gauge transformations always exist between differential equations or systems describing pseudospherical surfaces (resp. spherical surfaces). The local gauge transformation transforms a generic solution of one into any generic solution of the other.NEWLINENEWLINENEWLINEThe theory is applicable to some known equations: Nonlinear Schrödinger equations (NLS\(^+\) and NLS\(^-\)), \(iq_t+q_{xx}\pm 2|q|^2q=0\), the HF model, that is, the Schrödinger flow of maps into \(S^2\hookrightarrow \mathbb R^3\), the Landau-Lifschitz equation for an isotropic chain \(\mathbf S_t=S\times S_{xx}\) and etc.