| Scope and form: Lectures and exercises based on homework. |
| Evaluation: Oral presentation and approval of reports
|
| Examination: Pass/fail |
| Prerequisites: Master's degree or graduate students doing Thesis work. Medium level of mathematical physics. Experience in reading research papers. |
| Aim: Selected topics from advanced nonlinear dynamics. |
| Contents: 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. |
| 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/02907 |
| Signup: Registration to: Mads Peter Sørensen, Informatics and Mathematical Modelling, DTU, Building321, DK-2800 Kgs. Lyngby. E-mail: mps@imm.dtu.dk |
| Updated: 20-08-2001 |
