The geometric notion of some differential systems that characterise surfaces with constant negative curvature is studied in this paper. Furthermore, we research some non-linear partial differential equations and give them a definition of a family of constant Gaussian curvature-1 pseudo-spherical surfaces.

**Author(s) Details**

**Prof. G. M. Gharib
**Mathematics Department, College of Science, Zarqa University, Zarqa, Jordan.

**R. Z. Saadeh
**Mathematics Department, College of Science, Zarqa University, Zarqa, Jordan.

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