On differential equations derived from the pseudospherical surfaces. (English) Zbl 1472.35343

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.


35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35L71 Second-order semilinear hyperbolic equations
15A69 Multilinear algebra, tensor calculus
Full Text: DOI


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