School of Mathematics, Trinity College

Course 345 - Introduction to Solitons (click for more information)


Attention:: Revision class will take place on June 4, 2008 at 14:00 in Seminar Room, Hamilton Building



Instructor

Dr. Yakov M. Shnir
Office: 2.45 Lloyd Building
Phone:  01 896 1267
Office Hours: email for appointment
E-mail: shnir@maths.tcd.ie


Class Meetings

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


Course outline:

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.


Homework

Problems will be given every second week on Monday and are due at the BEGINNING of the class on Monday the following week.
Students can collaborate on their homework, however, each student should hand in her or his own copy of solutions.

Problem Sets in Postscript:


Sheet 1 Sheet 2 Sheet 3 Sheet 4


Problem Sets in PDF:


Sheet 1 Sheet 2 Sheet 3 Sheet 4