MATH584's home page

MATH 584-TOPICS IN MATHEMATICAL PHYSICS II

Spring 1999, Spring 2005

Text Book :
Maciej Blaszak, Multi-Hamiltonian Theory of Dynamical Systems , Springer, Berlin-Heidelberg, 1998.
Peter J. Olver , Applications of Lie Groups in Differential Equations , Springer-Verlag New York , 1986 (First Edition)

Other Books :
1. Peter J. Olver , Equivalence, Invariants and Symmetry , Cambridge University Press, 1995.
2. Giuseppe Gaeta, Nonlinear Symmetries and Nonlinear Equations , Kluver Academic Publishers, Dordreht ,1994.
3. W.I. Fushchich , W.M. Shtelen and N.I. Serov, Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics , Kluver Academic Publishers, Dordreht 1989.
4. G.W. Bluman and S. Kumei , Symmetries and Differential Equations , Springer, New York, 1989.

Content of the course
Second Semester is mainly on the generalized symmetries of (ordinary and partial) differential equations.
We shall study first two chapters of the book of Blaszak and
the remaining three chapters of the Olver's book.

Course Schedule

  • Wednesday 8.40-10.30 SAZ21
  • Friday 10.40-12.30 SAZ21

    Homework

    1. Homework Set 1

    Course Syllabus

    01. Jan. 25 - Generalized symmetries
    02. Feb. 01 - Generalized symmetries
    03. Feb. 08 - Recursion operators
    04. Feb. 15 - Generalized symmetries and conservation laws
    05. Feb. 22 - The variational complex
    06. Mar. 01 - Poisson brackets
    07. Mar. 08 - Symplectic structure
    08. Mar. 15 - First Integrals and reduction
    09. Mar. 22 - Poisson brackets for evolution equations
    10. Apr. 05 - Symmetries and conservation laws of evolution eqs.
    11. Apr. 12 - Recursion operators
    12. Apr. 19 - Recursion operators
    13. Apr. 26 - Bi-Hamiltonian systems
    14. May. 03 - Bi-Hamiltonian systems
    Metin Gürses
    Office: fen A126
    Bilkent University
    Bilkent, Ankara 06533 Turkey
    Phone:
    Office: (312) 2901924
    Home: (312) 2664560
    Fax:(312) 2664579
    Office: (90)(312) 2901924
    Email:gurses@fen.bilkent.edu.tr
    Home:Bilkent Universitesi Lojmanlari 8/3
    Bilkent, Ankara 06533 Turkey


    -------------- o -------------

    End of MATH584's Home Page