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
(Mainly nonlinear advection equation and the method of characteristics)
pdf (15 pages)
Handwritten notes on flood waves  (not discussed during the course)
These are meant to give a physical illustration of the use of the method of characteristics different from traffic flow theory.
pdf (4 pages)
 Illustration of 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
(Mainly advection-diffusion and Korteweg-de Vries equations)
pdf (14 pages)
When, as in KdV equation, dispersion dominates over viscosity, after wave breaking, a dispersive shock wave is formed, such as seen e.g., on Dordogne river Mascaret de St Pardon

 

TUTORIAL #1 TUTORIAL #2
solution_tuto1 solution_tuto2

previous exams

2017-2018 exam solution
2018-2019 exam solution
2019-2020 exam solution
2020-2021 exam solution

 

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