F7780 Nonlinear waves and solitons

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites
Basics notion on partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is intended to be an introduction to the physics of nonlinear waves, especially solitons.

The main objective of the course is to provide the students with the ability to
- list and describe fundamental principles and basic methods of nonlinear dynamics
- apply this knowledge to solve particular problems
Syllabus
  • 1)Summary of basic knowledge from the linear wave theory.
  • 2)Elementary solutions of the Burgers and Korteweg-de Vries equations.
  • 3)Sturm-Liouville problem and soliton solutions of the KdV equation.
  • 4)Inverse scattering method and KdV equation.
  • 5)Nonlinear Toda lattice and Fermi-Pasta-Ulam problem.
  • 6)Sinus-Gordon equation, topological solitons.
Literature
  • DRAZIN, Philip G. and Robin S. JOHNSON. Solitons : an introduction. Cambridge: Cambridge University Press, 1989, xii, 226. ISBN 0521336554. info
  • NETTEL, Stephen. Wave physics : oscillations - solitons - chaos. 2nd corr. enl. ed. Berlin: Springer-Verlag, 1995, 252 s. ISBN 3540585044. info
  • DODD, R. K. Solitons and nonlinear wave equations. Moskva: Mir, 1988, 694 s. ISBN 5-03-000732-6. info
Teaching methods
Lecture + seminars. Individual preparation of a paper for presentation in a seminar.
Assessment methods
oral testing of the lecture topics + successful presentation of the prepared paper
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
General note: L.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2002, Spring 2004, Spring 2006, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, Spring 2020, Spring 2022, Spring 2024.