Abstract and Applied Analysis

On Differential Equations Derived from the Pseudospherical Surfaces

Hongwei Yang, Xiangrong Wang, and Baoshu Yin

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 381717, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606303

Digital Object Identifier
doi:10.1155/2014/381717

Mathematical Reviews number (MathSciNet)
MR3200781

Zentralblatt MATH identifier
07022270

Citation

Yang, Hongwei; Wang, Xiangrong; Yin, Baoshu. On Differential Equations Derived from the Pseudospherical Surfaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 381717, 9 pages. doi:10.1155/2014/381717. https://projecteuclid.org/euclid.aaa/1412606303


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