Differential equations, symmetries and groups

Lecturer:

Libor Šnobl (gar.)

Tutor:

Libor Šnobl (gar.)

Supervisor:

Department of Physics

Synopsis:

The purpose of the lecture is to teach students computation of symmetries of the differential equations.

Requirements:

01MAA34, 01DIFR, 02TEF12

Syllabus of lectures:

1. Symmetries in physics and mathematics

2. Groups.

3. Local Lie groups.

4. Group action.

5. Lie point transformations.

6. Symmetries of equations.

7. Condition for infinitesimal symmetries.

8. Symmetries of the Burgers equation

Syllabus of tutorials:

1. Calculation of symmetries of a given equation (Heat equation, KdV equation, ...)

2. Interpretation of the symmetries

3. Determination of the Lie algebra of the symmetries

4. Symmetry reduction

Study Objective:

Knowledge:

Lie symmetries of differential equations

Abilities:

Computation of point symmetries of differential equations and their application in solution of given ODEs and PDEs.

Study materials:

Key references:

[1] P.J.Olver, Applications of Lie Groups to Differential Equations, Springer 2000

[2] P.E. Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide (Cambridge Texts in Applied Mathematics), CUP 2000

Recommended references:

[3] N.Kh. Ibragimov: Group analysis of ordinary differential equations and

the invariance principle in mathematical physics, Uspekhi Mat Nauk 47:4 (1992) 83-144 Russian Math. Surveys 47:4 (1992) 89-156

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• FNSPE Prospectus BC level (!)