2018/2019
Research Seminar "Introduction to the Theory of Integrable Equations"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Instructors:
Andrei Pogrebkov
Language:
English
ECTS credits:
3
Contact hours:
42
Course Syllabus
Abstract
Creation and development of the theory of integrable equations is one of main achievements of the mathematical physics of the fall of the previous century. In our times ideas and results of this theory penetrate in many branches of the modern mathematics: from string theory to the theory of Riemann surfaces.
Learning Objectives
- The seminar is intended to introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk.
Expected Learning Outcomes
- Successful participants imporve their presentation skills and prepare for participation in research projects in the subject area.
Course Contents
- Commutator identities on associative algebras;
- d-problem and dressing operators;
- Lax pairs;
- Kadomtsev - Petviashvili equation;
- Soliton solutions of the KP equation;
- Two-dimensional reduction:
- KdV equation;
- Details of the Inverse scattering transform for KdV equation;
- Soliton solutions of the KdV equations, their properties;
- Вispersion relation and integrals of motion;
- IST as canonical transformation.
Assessment Elements
- Cumulative gradecumulative grade is proportional to number of tasks solved.
- Final exam
Bibliography
Recommended Core Bibliography
- Babelon, O., Bernard, D., & Talon, M. (2003). Introduction to Classical Integrable Systems. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=120350
- Nirov, K. S., & Razumov, A. V. (2018). Vertex Models and Spin Chains in Formulas and Pictures. https://doi.org/10.3842/SIGMA.2019.068
Recommended Additional Bibliography
- Baxter, R. J. (2007). Exactly Solved Models in Statistical Mechanics (Vol. Dover ed). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1152951