Advanced Nonlinear Physics

lecture 1: generalities commented slides pdf version of the slides
lecture 2: traffic flow and method of characteristics commented slides pdf version of the slides
lecture 3: viscous shocks commented slides
solution exercice 1a, 1srt tutorial
solution exercice 1d, 1srt tutorial
solution exercice 2.3, 1srt tutorial
pdf_version_of the slides
lecture 4: advection-diffusion and KdV commented slides pdf version of the slides
lecture 5: NLS recorded lecture properly drafted typed notes
lecture 6: reaction-diffusion typed_notes


Handwritten notes  for the course I                                                                                                                          pdf (15 pages)
(Mainly nonlinear advection equation and the method of characteristics)
Handwritten notes on flood waves  (not discussed during the course)                                                                  pdf (4 pages)
These are meant to give a physical illustration of the use of the method of characteristics different
from traffic flow theory, but also to illustrate the importance of the subject: cf the video showing a
flood submerging a bridge in less than 3mns (St Jean du Gard, 19/09/2020, cortesy of E. Pratlong)                                                                                                                                                                 submersion wave
Handwritten notes for the course ii                                                                                                                           pdf (14 pages)
(Mainly advection-diffusion and Korteweg-de Vries equations)
When, as in KdV equation, dispersion dominates over viscosity, after wave breaking one
observes a dispersive shock wave such as seen e.g., on Dordogne river                                                               Mascaret de St Pardon


solution_tuto1 solution_tuto2

previous exams

2017-2018 exam solution
2018-2019 exam solution
2019-2020 exam solution


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