UE1 Introduction to the theory and applications of S9 SM2NLP

Objectives: Introduction to the methods of integration of partial differential equations admitting soliton solutions.

Organization: CM: 15 h, TD: 10 h.

Necessary background: general knowledge of physics

Topics of the course: Non-linear waves, effects of dispersion and dissipation, solitary waves. Lattice solitons, Toda chain, the Fermi-Pasat-Ulam phenomenon, spin waves. Hydrodynamical solitons, equations of Kordeweg-de Vries and sin-Gordon, solitons in optical fibers. Mathematical aspects – the Lax formulation and the inverse scattering method.

Skills to be achieved:
Understanding the general notion of soliton.
Ability to integrate partial differential equations of certain types.

Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%