Initial Value Problems of the Sine-Gordon Equation and Geometric Solutions
| dc.creator | Toda, Magdalena | |
| dc.date | 2003-07-20 | |
| dc.date | 2005-02-28 | |
| dc.date.accessioned | 2026-07-07T04:59:47Z | |
| dc.date.available | 2026-07-07T04:59:47Z | |
| dc.description | Recent results using inverse scattering techniques interpret every solution $ϕ(x,y)$ of the sine-Gordon equation as a non-linear superposition of solutions along the axes $x=0$ and $y=0$. Here we provide a geometric method of integration, as well as a geometric interpretation. Specifically, every weakly regular surface of Gauss curvature $K=-1$, in arc length asymptotic line parametrization, is uniquely determined by the values $ϕ(x,0)$ and $ϕ(0,y)$ of its coordinate angle along the axes. Based on a generalized Weierstrass pair that depends only on these values, we prove that to each such unconstrained pair of differentiable functions, there corresponds uniquely an associated family of pseudospherical immersions; we construct these immersions explicitely. | |
| dc.identifier | https://arxiv.org/abs/math/0307270 | |
| dc.identifier | http://arxiv.org/abs/math/0307270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68126 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53A10, 58E20 | |
| dc.title | Initial Value Problems of the Sine-Gordon Equation and Geometric Solutions | |
| dc.type | text |