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04225 Nonlinear partial differential equations, solitons
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Danish title: Ikke-lineære partielle differentialligninger, solitoner
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| Type: Å, Language: E |
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Credit points:
5 point |
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| | | Previous course: C0315 |
| Offered by:
Department of Mathematical Modelling
(IMM) |
| No credit points with: C0315 |
| Prerequisite: 04211/01248/10231/04201 |
| Desirable: 04202 (senest samtidig) |
| Recommended semester:
4th -7th semester |
| Scope and form: 2 modules, lecture and 2 hours of excercises and group work. |
| Examination:
Homework assignments and report on selected topic.
(13 point scale
) |
| Remarks: Relations to other courses: 10479 Plasmaph..., 57345 Wave Hydro..., 10227 Superc..., 10247 Non-linear..., 48342 Optical..., 36210 Transp..., 77263 Fluid Mechanics. |
| Contact person: |
Peter Leth Christiansen, IMM, Building 305, Tel. +45 4525 3096 |
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| Aim: To describe physically important non-linear wave phenomena. |
| Contents: Derivation of non-linear partial differential equations from hydrodynamics, optics, solid state physics, molecular dynamics, and neurobiology. Solitary waves as a balance between nonlinearity and dispersion or between nonlinearity and dissipation. Solitary waves and solitons, non-linear interactions, decomposition into solitons and radiation, and conservation theorems. Technological and biological applications of solitary waves. Analytical and numerical methods. Generalized separation of variables. Bäcklund-transformations, inverse scattering techniques, perturbation theory and similarity solutions. Nonlinear diffusion as a paradigm for nonlinear effects in neurobiology. Spatio-temporal competition between order and chaos. Examples of recent research. |
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