Integrable Systems (EM6)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	EM6
Semester	1
Course Title	Integrable Systems
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

Integrable systems are nonlinear differential equations which, in principle, can be solved analytically. This means that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare - most nonlinear differential equations admit chaotic behavior and no explicit solutions can be written down. Integrable systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics. The main topics treated in the course, and the expected skill obtained by the students, are: Integrability of ODEs: Hamiltonian formalism, the Arnold-Liouville theorem, Painleve analysis. Integrability of PDEs: Solitons, Inverse Scattering Transform.

General Competences

Adapting to new situations Decision-making Working independently Team work

Syllabus

Integrability in classical mechanics, Painleve analysis, Fourier transforms, the Inverse Scattering Transform and Soliton theory.

Teaching and Learning Methods - Evaluation

Delivery	In class
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Self study 78 Homework - Projects 70.5 Course total 187.5
Student Performance Evaluation	Weekly assignments Final project

Attached Bibliography

• P. G. Drazin, R. S. Johnson, Solitons: An Introduction, Cambridge University Press, 1989.
• M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM 1981.
• Προσωπικές σημειώσεις του διδάσκοντα.