| 02655 Non-linear Partial Differential Equations. Solitons. Biomath |
| Danish title: Ikke-lineære partielle differentialligninger. Solitoner. Biomatematik |
|
Language: English ECTS-creditpoints: 10, External examination.
|
|
|
Exam schedule:
|
F1-B (maj 28 2002), E1-B (dec 11 2001) |
| Recommended semester: 4th -7th semester |
| Scope and form: Lectures and exercises |
| Evaluation: Oral exam
|
| Examination: 13-scale |
| Previous course: 04224 + 04225 |
| Prerequisites: Partial differentiation, basic nonlinear dynamics. |
| No credit points with: C0315 / C0334 |
| Aim: To describe modern methods and results for important non-linear wave phenomena and from Mathematical Biology. |
| Contents: Non-linear partial differential equations from hydrodynamics, optics, solid state physics, and molecular dynamics. Balance between nonlinearity and dispersion. Solitary waves and solitons, non-linear interactions, decomposition into solitons and radiation. Conservation theorems. Technological applications of solitary waves. Analytical methods for integrable systems: generalized separation of variables, Baecklund transformation, inverse scattering techniques. Perturbation theory and similarity solutions. Numerical methods. Spatio-temporal competition between coherent structures and chaos. Continuous and discrete systems. Lattice dynamics and molecular crystals. Quantum solitons. Nonlinear diffusion equations. Balance between nonlinearity and diffusion, nerve physiology, excitable media, brain dynamics, biological solitons, biomolecular dynamics. |
Remarks: Lectures by visiting professors are included.
Textbook: Alwyn C. Scott with contributions from Mads Peter Sørensen and Peter Leth Christiansen, Nonlinear Science, Emergence and Dynamics of Coherent Structures, Oxford University Press 1999.
Relations to other courses (with old course numbers in parenthesis):
02615 Non-linear Wave Dynamics
02653 Non-linear Dynamical Systems with Applications
(10227) Superconductivity
(10247) Non-linear Optics
(10477) Plasma Physics 1 (Fusion Plasma Physics)
(36210) Transport Processes
(77256) Basic Fluid Mechanics
(xxxxx) Biological Physics |
| Contact: Peter Leth Christiansen, building 305, (+45) 4525 3096, plc@imm.dtu.dk |
| Department: 002 Informatics and Mathematical Modelling |
| Course URL: http://www.imm.dtu.dk/courses/02655 |
| Keywords: Non-linear partial differential equations, solitons, non-linear science, non-linear diffusion, mathematical biology |
| Updated: 07-05-2001 |
|
|
