MU03259 Geometric Theory of Partial Differential Equations II

Mathematical Institute in Opava
Summer 2016
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
MU03258 Geometric Theory of PDE I
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.
  • 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.
    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
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.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2016, recent)
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