1. SylabUZ
2. Faculty of Physics and Astronomy
3. winter term 2018/2019
4. Physics and Astronom - PhD studies
5. Lecture III-P

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Lecture III-P - course description

Aim of the course

Introduce students to to wave phenomena, in particular to nolinear waves.

Prerequisites

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Basic knowledge of classical mechanics and fluid dynamics.

Scope

• Waves in nature

• Origin of nonlinear wave equations

• Universal wave equations

• Korteweg-de Vries equation

• Kadomtsev – Petviashvili equation

• Nonlinear Schrödinger equation

• Properties of solutions to nonlinear wave equations

• Soliton solutions

• Periodic solutions

• Analytic and numerical solutions.

• Lagrange and Hamilton formalism for several kinds of nonlinear wave equations

• Invariants and conservation laws.

Teaching methods

Lecture

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Exam – description of some theoretical problems

Recommended reading

1. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge University Press, Cambridge, 2000 (second edition).

2. G.B. Whitham, Linear and Nonlinear Waves, Wiley, 1974.

3. A. Karczewska, P. Rozmej, Shallow water waves – extended Korteweg – de Vries equations, Oficyna Wydawnicza UZ, 2018.

Further reading

Notes

Modified by dr Joanna Kalaga (last modification: 11-07-2018 13:24)