Lobachevská geometrie a solitérní vlny
| Thesis title in Czech: | Lobachevská geometrie a solitérní vlny |
|---|---|
| Thesis title in English: | Lobachevsky geometry and solitary waves |
| English key words: | Lobachevsky geometry; Solitons; Singular embeddings; |
| Academic year of topic announcement: | 2017/2018 |
| Thesis type: | project |
| Thesis language: | |
| Department: | Institute of Particle and Nuclear Physics (32-UCJF) |
| Supervisor: | prof. Alfredo Iorio, Ph.D. |
| Author: |
| Guidelines |
| The student needs to
- have a basic knowledge of elementary differential geometry - have a basic knowledge of differential equations - be willing to work towards classification of solutions Skills to plot with and manage Mathematica packages are welcome, but not necessary. |
| References |
| L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, (Princeton University Press, Princeton, 1909)
A. Ovchinnikov, Gallery of pseudospherical surfaces, in Nonlinearity and Geometry, eds. D. Wojcik and J. Cieslinnski (Polish Scientific Publishers PWN, Warsaw, 1998), pp. 41–60 R. McLachlan, A Gallery of Constant Negative Curvature Surfaces, THE MATHEMATICAL INTELLIGENCER, 16 (1994) 31 R. Rajaraman, Solitons and Instantons, an introduction to solitons and instantons in quantum field theory, 2nd edition (Elsevier Science, Amsterdam, 1987) S. Coleman, Classical lumps and their quantum descendants, in Aspects of Symmetry, selected Erice lectures, (Cambridge University Press, Cambridge, 1985) |
| Preliminary scope of work |
| The infinite number of surfaces of constant negative curvature realize, in our Euclidean three-space, portions of the infinite Lobachevsky plane. These surfaces are fascinating for many purely mathematical reasons. For instance, they have to include some form of singularities, as Hilbert theorem proves. On the other hand, among the physical applications, one is particularly interesting. That is the relationship between these surfaces and the sine-Gordon solitons. The student will clarify this link, and present a list of known correspondences that she/he will be able to find in the literature. If possible, she/he will provide a clarification of the role of the above mentioned singularities in the physics of corresponding solitons. |