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