On differential equations derived from the pseudospherical surfaces
Summary: We construct two metric tensor fields; by means of these metric tensor fields, sinh-Gordon equation and elliptic sinh-Gordon equation are obtained, which describe pseudospherical surfaces of constant negative Riemann curvature scalar \(\sigma\) = \(-\)2, \(\sigma\) = \(-\)1, respectively. By employing the Bäcklund transformation, nonlinear superposition formulas of sinh-Gordon equation and elliptic sinh-Gordon equation are derived; various new exact solutions of the equations are obtained.
scientific article; zbMATH DE number 7022270
scientific article