F7780 Non-Linear Waves and Solitons

Exercises: Wednesdays 15:00-16:00.
Lectures: Wednesdays 16:00-18:00.

Both lectures and exercises take place in Prof. Michal Lenc's office "03028", 3rd floor, building 6.

Course Plan, Spring 2016:

Wednesday 17.02.16
No classes.

Wednesday 24.02.16
KdV equation [DZ2] Chap. 1-2; No exercises;

Wednesday 02.03.16
Pseudo-differential operators, Lax equation [JH1] Chap. 12; No exercises;

Wednesday 09.03.16
Scattering [DZ2] Chap. 3.1-3.2; Exercises: [DZ2] Q2.1i+ii;

Wednesday 16.03.16
Scattering [DZ2] Chap. 3.3; Exercises: [DZ2] Q3.4i with discontinuities instead at x=+/-1;

Wednesday 23.03.16
Scattering [DZ2] Chap. 4.1-4.4; Exercises: [DZ2] Q3.4ii with discontinuities instead at x=+/-1;

Wednesday 30.03.16
Marchenko equation [DZ2] Chap. 3.4; Exercises: [DZ2] Q4.1i + Derive eq. (4.19).

Wednesday 06.04.16
Reflectionless potentials [DZ2] Chap. 4.5; Supersymmetry & QM [CKS] Chap. 2; Exercises: [DZ2] Q4.4i;

Wednesday 13.04.16
Conservation laws [DZ2] Chap. 5.1; 5.1.1; Hamiltonian formulation: Faddeev-Jackiw method versus Dirac 2nd class contraints [DZ2] Chap. 5.1.3; Exercises: [DZ2] Q4.4ii + Q4.8;

Wednesday 20.04.16
Infinite Tower of Conservation Laws [DZ2] Chap. 5.1.2; Exercises: [DZ2] Q5.5 + Q5.8;

Wednesday 27.04.16
Lax equation [DZ2] Chap. 5.2; Hirota bilinear equation [DZ2] Chap. 5.3; Baecklund transformations [DZ2] Chap. 5.4.1; Exercises: [DZ2] Q5.15;

Wednesday 04.05.16
Solitons in 1+1 dimensions [tHB] Chap. 1; Vortices in 2+1 dimensions [tHB] Chap. 2; Exercises: [DZ2] Q5.14;

Wednesday 11.05.16
No lectures.

Wednesday 18.05.16
Colloquium.

Wednesday 25.05.16
No lectures.

Colloquium titles

Wednesday 18.05.16
15:00 Patrik: Great red spot on Jupiter as a soliton
15:30 Tomas: Solitons in Ricci flow
16:00 Jan S: Solitons in optical fibres
16:30 Martin: Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation, arXiv:arXiv:1205.5917
17:00 Katerina: The KdV hierarchy in optics
17:30 Jakub: Derivation of KdV equation from Euler's equations
18:00 Jan M: Non-linear Schroedinger equation

References:

[DZ2]: P.G. Drazin and R.S. Johnson, "Solitons: An Introduction", Eds. 2, 1989.
[JH1]: Jens Hoppe, "Lectures on Integrable Systems", Eds. 1, Lecture notes in Physics, Springer, 1992.
[CKS]: F. Cooper, A. Khare, & U. Sukhatme, "Supersymmetry and Quantum Mechanics", Phys. Rept. 251 (1995) 267 , arXiv:hep-th/9405029 .
[tHB]: G. 't Hooft and F. Bruckmann, "Monopoles, Instantons and Confinement", arXiv:hep-th/0010225 .