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On Differential Equations Derived from the Pseudospherical Surfaces

Author

Listed:
  • Hongwei Yang
  • Xiangrong Wang
  • Baoshu Yin

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.

Suggested Citation

  • Hongwei Yang & Xiangrong Wang & Baoshu Yin, 2014. "On Differential Equations Derived from the Pseudospherical Surfaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:381717
    DOI: 10.1155/2014/381717
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    References listed on IDEAS

    as
    1. G. M. Gharib, 2012. "Surfaces of a Constant Negative Curvature," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-17, October.
    2. Xia, Tiecheng & Chen, Xiaohong & Chen, Dengyuan, 2005. "Darboux transformation and soliton-like solutions of nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 889-896.
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