MU:MU03259 Geometric Theory of PDE II

MU03259 Geometric Theory of Partial Differential Equations II

Mathematical Institute in Opava
Summer 2019

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

Prerequisites

MU03258 Geometric Theory of PDE I
MU/03258

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

Course objectives

See MU/03258. In the second semester we will mostly deal with the conservation laws, their relations with symmetries, and the associated structures.

Syllabus

Conservation laws, cosymmetries and their computation.
Basics of calculus of variations. Symmetries of variational problems. The Noether theorems.
Hamiltonian structures of evolution systems of partial differential equations and their properties. Bihamiltonian systems and their integrability. Recursion operators and symplectic structures.
Zero curavture representations and their applications; the spectral parameter; gauge transformations. Lax representations and introduction to the inverse scattering method.

Literature

recommended literature

A.M. Vinogradov, I.S. Krasil'ščik, eds. Simmetrii i zakony sochraneniya uravnenij matematičeskoj fiziki. Faktorial, Moskva, 1997. info
P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
G. W. Bluman a S. Kumei. Symmetries and Differential Equations. Springer, New York, 1989. info

not specified

C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

Teacher's information

Oral exam; further requirements to be specified in the course of the semester.