Course title: Nonlinear and stochastic dynamics. Modelling of technical systems and biomathematics.
Course responsible person: Mads Peter Sørensen.
Lecturers: P.L. Christiansen, M.P. Sørensen and J.J. Rasmussen.
Institution: Technical University of Denmark.
Danish name of institution: Danmarks Tekniske Universitet.
Official abbreviation: DTU.
Faculty: Communications, Informatics and Mathematics.
Department: Institute of Mathematical Modelling (IMM).
Course period 8/10-12/12, 1997.
Dates, if known at time: 8/10-10/10, 12/11-14/11 and 12/12, 1997.
Time of day: 9:00-17:00.
Days of week: Wednesday, Thursday, and Friday.
Course arrangement: 2 times 3 full days. December 12, 1997, is reserved for evaluation.
Teaching arrangement: Lectures and exercises based on homework.
Language: English.
Place: Institute of Mathematical Modelling, Building 305, seminar room 027, The Technical University of Denmark, DK-2800 Lyngby.
Number of participation hours: 48 (including evaluation)
Number of actual working hours: 140
Estimated part of obligatory 1/2 year of courses: 20%.
The course is part of the following Ph.D.-program: Mathematics.
The course is in this program: Optional.
Is the course open to other than Ph.D.-students: Yes.
If yes, then which students: Higher-level undergraduates.
Is it mandatory to be enrolled in one or more specific Ph.D.-programs as a prerequisite for participation: No.
If yes, then which ones: -
Course content (five keywords): Nonlinear dynamics, solitons, optical and solid state physics, biomolecular dynamics, stochastic systems.
Classification of course content according to UDK-number (library classification): -
Course type: Theory and application oriented course.
Basic literature to indicate type of course and content:
R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, and H.C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, 1982.
P.G. Drazin and R.S. Johnson, Solitons: an introduction, Cambridge University Press, Cambridge, 1989
A.C. Newell and J.V. Moloney, Nonlinear Optics, Addison-Wesley Publishing Company, 1992.
G.L. Lamb, Elements of soliton theory, John Wiley and Sons, New York, 1980.
Course material:
Lecture notes, papers and book chapters.
Course fee: None.
Course costs, if any other than fee (for materials etc.): 150 Dkr.
Participants obligation during course: Presentation and written report.
Type of evaluation: Participation, report and oral presentation (12/12 1997) of report.
Evaluation result: passed/not-passed.
Course participation documentation: Course diploma.
Registration to:
Mads Peter Sørensen,
E-mail address: mps@imm.dtu.dk
Deadline: Friday, September 26, 1997.
Information on enrollment will be given Friday, September 27, 1996.
The course will be repeated, if this is the case, then how or when: October-December 1997. (Content and form may be changed).
Further particulars on the course can be obtained at the following:
Mads Peter Sørensen, Institute of Mathematical Modelling, Bldg. 321, Technical University of Denmark, DK-2800 Lyngby.
E-mail: mps@imm.dtu.dk
Phone: (+45) 4525 3094
Fax: (+45) 4593 1235
Peter Leth Christiansen, Institute of Mathematical Modelling, Bldg. 321, Technical University of Denmark, DK-2800 Lyngby.
E-mail: lg@imm.dtu.dk
Phone: (+45) 4525 3096
Fax: (+45) 4593 1235
Course description (max 250 words): Selected topics from advanced nonlinear dynamics: General inverse scattering theory (AKNS) for e.g. sine-Gordon, nonlinear Schrödinger, Korteweg-de Vries equations and discrete systems. Soliton perturbation theory based on variational methods and collective coordinate methods. Coherent structures and chaos. stochastic perturbations and nonlinear diffusion. Quantization of discrete systems.
The derivation of nonlinear partial differential equations for optical fibres and erbium doped fibre amplifiers, long Josephson junctions and long biomolecular systems such as proteins and DNA strings. Inclusion of thermal noise. The classical "Discrete Self Trapping" (DST) equation and other anharmonic lattice equations. Quantization methods. Collapse phenomena in one and two dimensions. Nonlinear models of quantum well lasers and fibre ring lasers to generate ultra short light pulses for optical communications systems. Anisotropic energy gap models of high temperature superconducting materials.
Course plan: October 9-11 the students must attend lectures and exercises at the Institute of Mathematical Modelling (IMM). Course material will be handed out to the students for selfstudy and exercises. November 13-15 the students must attend lectures and exercises at IMM. Based on research papers the students prepare a short report (5 pages) and a talk (1/2 hour) to be presented on December 13, 1996. The students must attend all oral presentations on December 13.
Litterature: Lecture notes and selected papers.