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Pseudospherical Surfaces and Evolution Equations in Higher Dimensions


Affiliations
1 Mathematics Department, Minia University, Egypt
2 Mathematics Department, Fayoum University, Egypt
 

In this paper, the study of evolution equations with two independent variables which are related to pseudospherical surfaces in R3, is extended to evolution equations with more than two independent variables. Equations of the type.Β 
𝒖𝒙𝒕=Ξ¨(𝒖,𝒖𝒙,… … ..,Β βˆ‚π’Œ 𝒖/βˆ‚ π’™π’Œ,π’–π’š,… … …,βˆ‚ π’ŒΚΉπ’–/βˆ‚ π’šπ’ŒΚΉ)
are studied and characterized. Some features and results on properties of these equations are given via this study.

Keywords

Evolution Equations, Pseudospherical Surfaces, Riemannian Manifold and Solitons.
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  • Pseudospherical Surfaces and Evolution Equations in Higher Dimensions

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Authors

M. F. El-Sabbagh
Mathematics Department, Minia University, Egypt
K. R. Abdo
Mathematics Department, Fayoum University, Egypt

Abstract


In this paper, the study of evolution equations with two independent variables which are related to pseudospherical surfaces in R3, is extended to evolution equations with more than two independent variables. Equations of the type.Β 
𝒖𝒙𝒕=Ξ¨(𝒖,𝒖𝒙,… … ..,Β βˆ‚π’Œ 𝒖/βˆ‚ π’™π’Œ,π’–π’š,… … …,βˆ‚ π’ŒΚΉπ’–/βˆ‚ π’šπ’ŒΚΉ)
are studied and characterized. Some features and results on properties of these equations are given via this study.

Keywords


Evolution Equations, Pseudospherical Surfaces, Riemannian Manifold and Solitons.