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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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Language: English
Credit points: 5 |
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| Type: | Ph.D.-level, Open University
Language: English |
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Previous course: C0315
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No credit points with: C0315
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Prerequisite: 04211/01248/10231/04201
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Recommended semester: 4th -7th semester
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Scope and form: 2 modules, lecture and 2 hours of excercises and group work.
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Examination: Oral exam (13-scale)
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Remarks: Relations to other courses: 10479 Plasmaph..., 57345 Wave Hydro..., 10227 Superc..., 10247 Non-linear..., 48342 Optical..., 36210 Transp..., 77263 Fluid Mechanics.
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URL: http://www.imm.dtu.dk/documents/users/plc/Kurser/04225/template.html
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Department: Informatics and Mathematical Modelling
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Aim: To describe physically important non-linear wave phenomena.
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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. Biomolecular dynamics (DNA and alpha.helix protein). Quantum solutions. Examples of recent research.
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