Application of soliton theory to the construction of pseudospherical surfaces in \(\mathbb{R}^ 3\). (English) Zbl 0810.53003
Summary: This paper studies the geometry of pseudospherical surfaces from the point of view of Lorentz harmonic maps from the Minkowski plane into \(S^ 2\). After giving appropriate definitions, it is shown that such a map is the Gauss map of a pseudospherical surface. A natural subclass of harmonic maps is isolated and studied using well developed techniques of soliton theory. Then follows a numerical investigation based on these techniques. Examples that fall outside of the aforementioned subclass are also considered.
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35Q40 | PDEs in connection with quantum mechanics |
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