| 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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Desirable: 04202 (not later than the same semester)
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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: Lectures by visiting professors are included.
Textbook: A.Scott et al. Nonlinear Science, Oxford University Press, (1999).
Relations to other courses:
04416 Nonlinear Wave Dynamics,
04421 Bifurcation and Chaos with Engineering Applications,
04426 Non-linear Stochastic Dynamics with Applications,
10227 Superconductivity,
10247 Non-linear Optics,
10477 Plasma Physics 1 (Fusion Plasma Physics),
36210 Transport Processes,
77256 Basic Fluid Mechanics.
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URL: http://www.imm.dtu.dk/courses/04225
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Department: Informatics and Mathematical Modelling
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Aim: To describe important non-linear wave phenomena.
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Contents: Derivation of non-linear partial differential equations from hydrodynamics, optics, solid state physics, and molecular dynamics. Solitary waves as a balance between nonlinearity and dispersion. 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. Spatio-temporal competition between order and chaos. Biomolecular dynamics (DNA and alpha.helix protein). Molecular crystals. Quantum solutions. Examples of recent research.
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