MU25014 Solution Methods for Nonlinear Partial Differential Equations

Mathematical Institute in Opava
Summer 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
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 (in Czech)
V předmětu budou podán přehled základních klasických a moderních metod řešení nelineárních parciálních diferenciálních rovnic a jejich systémů.
Syllabus
  • 1. Transdformations of variables: point and contact transformations. Jet spaces.
    2. Partial differential equations of first order. Complete solution, general solution, singular solution, characteristics.
    3. Systems of equations and equations of higher order. Compatibility, power series solutions, Cauchy theorem.
    4. Ampere method.
    5. Intermediate integrals. Darboux method.
    6. Baecklund transformation, coverings. Permutability and nonlinear superposition.
    7. Basic soliton equations and phenomenology of their solitons.
    8. Zero curvature representations, Lax pairs, introduction to solving of soliton equations.
Literature
    recommended literature
  • E. D. Belokolos, A. I. Bobenko, V. Z. Enolskii, A. R. Its a V. B. Algebro-geometrical approach to nonlinear integrable equations. info
  • D. Hilbert a R. Courant. Methods of Mathematical Physics, Vol. 2. Wiley, 1989. info
  • C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982. info
  • A. R. Forsyth. Theory of Differential Equations, Vol. 5, 6. Cambridge Univ. Press, 1906. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Summer 2016, Summer 2017, Summer 2018.
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