Dr. Yakov M. Shnir Office: 2.45 Lloyd Building Phone: 01 896 1267 Office Hours: email for appointment E-mail: shnir@maths.tcd.ie |
Lectures: | Monday |
12:00-12:50 | MacNeill Theatre, Hamilton Building |
McN3 |
Friday |
10:00-10:50 | Salmon
Lecture Theatre |
Sal1 | |
Lectures/Problem Session: | Friday |
12:00-12:50 | SNIAM Lecture Room | SNlr |
Introduction to history of solitons. Linear waves. D'Alembert's solution. Dispersion and dispersion relations, wave speed, wavelength, wave number. Linear superposition. Introduction to nonlinear wave phenomena. Burger's equation. The Korteweg and de Vries equation. The scattering and inverse scattering problems. The nonlinear Schrodinger equation, its soliton solutions. Two solitons solutions and their interactions. Further integrable non-linear differential equations, the Lax formulation. Hirota's method and Baecklund transformations. The Fermi-Pasta-Ulam problem. Models for dislocations in crystals. The sine-Gordon equation. Kink solution in 1+1 dimensional scalar model. Domain walls. Solitons in field theory. Topological classification. Ginzburg-Landau model. Abrikosov-Nielsen-Olesen vortex solution.