Linear and Nonlinear Waves (MAE747)

Από Wiki Τμήματος Μαθηματικών



School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Linear and Nonlinear Waves

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations


Is the Course Offered to Erasmus Students


Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The study of nonlinear systems has quietly and steadily revolutionized the realm of science over recent years. It is known that for nonlinear systems new structures emerge that have their features and peculiar ways of interacting. Examples of such structures abound in nature and include, amongst others: vortices (like tornadoes), solitons (bits of information used in optical fiber communications, water waves, tsunamis, etc), and chemical reactions. This course is intended as an introduction to the theory and of Nonlinear Waves and their applications. By the end of the course students will be able to:

  • highlight the major differences between linear and nonlinear waves and the special features of solitons.
  • Solve linear waves equations and understand the concept of a dispersion relation.
  • Construct similarity solutions.
  • use the inverse scattering transform and to construct analytical solutions.
General Competences
  • Search for, analysis and synthesis of data and information, with the use of the necessary technology.
  • Adapting to new situations.
  • Decision-making.


The linear wave theory, Burgers' equation, the Korteweg-de Vries (KdV) equation, travelling waves and the scattering problem for the KdV equation, the inverse scattering transform and solitons, the nonlinear Schrödinger equation, applications to water waves and optics.

Teaching and Learning Methods - Evaluation


Face to face

Use of Information and Communications Technology Yes
Teaching Methods
Activity Semester Workload
Lectures 39
Self study 78
Exercises 33
Course total 150
Student Performance Evaluation
  • Weekly homework
  • Final project
  • Final exam

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • Solitons: an Introduction, P. G. Drazin and R. S. Johnson, Cambridge University Press, 1989.
  • Γ. Δ. Ακρίβης και Ν .Δ. Αλικάκος, Μερικές Διαφορικές Εξισώσεις, Σύγχρονη Εκδοτική, 2012.
  • Εφαρμοσμένα Μαθηματικά, D. J. Logan, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.