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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 381717, 9 pages
http://dx.doi.org/10.1155/2014/381717
Research Article

On Differential Equations Derived from the Pseudospherical Surfaces

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
3Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China

Received 2 January 2014; Revised 19 March 2014; Accepted 21 March 2014; Published 24 April 2014

Academic Editor: Weiguo Rui

Copyright © 2014 Hongwei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.