Course: Geometric Theory of Partial Differential Equations II

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Course title Geometric Theory of Partial Differential Equations II
Course code MU/03259
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
unspecified
Recommended literature
  • A.M. Vinogradov, I.S. Krasil'ščik, eds. Simmetrii i zakony sochraneniya uravnenij matematičeskoj fiziki. Faktorial, Moskva, 1997.
  • C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982.
  • G. W. Bluman a S. Kumei. Symmetries and Differential Equations. Springer, New York, 1989.
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 5 Summer