VU Teorinės fizikos ir astronomijos institute, Goštauto 12, 433 auditorijoje pirmadieniais 13.30 skaitomas paskaitų ciklas "Solitons in Mathematical Physics and Field Theory".

Lektorius prof. Y. Shnir iš Minsko universiteto.

Paskaitos vyksta anglų kalba. Paskaitų medžiaga: Lecture1.pdf, Lecture2.pdf, Lecture2.pdf

Paskaitų ciklo "Solitons in Mathematical Physics and Field Theory" planas.

1. Introduction to the history of solitons.
2. Linear waves. D'Alembert's solution. Dispersion and dispersion relations, wave speed, wavelength, wave number. Linear superposition.
3. Introduction to nonlinear wave phenomena.
4. Burger's equation. The Korteweg-de Vries equation.
5. The scattering and inverse scattering problems.
6. The nonlinear Schr"odinger equation, its soliton solutions.
7. Two solitons solutions and their interactions.
8. Further integrable non-linear differential equations, the Lax formulation.
9. Hirota's method and B"acklund transformations
10. The Fermi-Pasta-Ulam problem.
11. Models for dislocations in crystals. The sine-Gordon equation.
12. Kink solution in the 1+1 dimensional $phi^4$ model. Domain walls.
13. Solitons in field theory. Topological classification.
14. The Ginzburg-Landau model. The Abrikosov-Nielsen-Olesen vortex solution.