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Timelike W‐Surfaces in Minkowski 3‐Space ℝ13 and the Sinh‐Gordon Equation

Author

Listed:
  • Nadia Alluhaibi
  • Rashad A. Abdel-Baky

Abstract

Let M and M∗ be two timelike surfaces in Minkowski 3‐space ℝ13. If there exists a spacelike (timelike) Darboux line congruence between each point of M and M∗, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh‐Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.

Suggested Citation

  • Nadia Alluhaibi & Rashad A. Abdel-Baky, 2022. "Timelike W‐Surfaces in Minkowski 3‐Space ℝ13 and the Sinh‐Gordon Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:7998748
    DOI: 10.1155/2022/7998748
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    References listed on IDEAS

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    1. Yunchuan Sun, 2014. "New Travelling Wave Solutions for Sine‐Gordon Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Yunchuan Sun, 2014. "New Travelling Wave Solutions for Sine-Gordon Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-4, April.
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