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Linear and Nonlinear Waves (MAE747)

Linear and Nonlinear Waves (MAE747)

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Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE747

Semester

7

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

Greek

Is the Course Offered to Erasmus Students

Yes

Course Website (URL) -

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.

Syllabus

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

Delivery

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 Eudoxus. Additionally:

  • 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.
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