F7780 Nonlinear waves and solitons

Faculty of Science
Spring 2012
Extent and Intensity
2/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Klaus Bering Larsen, Ph.D. (lecturer)
doc. Klaus Bering Larsen, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
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
Abstract
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
Key topics
  • 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)Sine-Gordon equation, topological solitons.
Study resources and 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
Approaches, practices, and methods used in teaching
Lecture + seminars. Individual preparation of a paper for presentation in a seminar.
Method of verifying learning outcomes and course completion requirements
oral testing of the lecture topics + successful presentation of the prepared paper
Language of instruction
English
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 2011 - only for the accreditation, Spring 2000, Spring 2002, Spring 2004, Spring 2006, Spring 2008, Spring 2010, spring 2012 - acreditation, Spring 2014, Spring 2016, Spring 2020, Spring 2022, Spring 2024, Spring 2026.
  • Enrolment Statistics (Spring 2012, recent)
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