On Differential Equations Derived from the Pseudospherical Surfaces

Hongwei Yang, Xiangrong Wang and Baoshu Yin

Abstract and Applied Analysis, 2014, vol. 2014, 1-9

Abstract:

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 σ = −2, σ = −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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:381717

DOI: 10.1155/2014/381717

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