MU25014 Solution Methods for Nonlinear Partial Differential Equations

Mathematical Institute in Opava
Winter 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Hynek Baran, Ph.D. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Timetable
Tue 14:45–16:20 205
  • Timetable of Seminar Groups:
MU25014/01: Mon 8:05–9:40 R1, P. Vojčák
Prerequisites (in Czech)
TYP_STUDIA ( N )
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
An overview of classical and modern methods to find exact solutions of nonlinear partial diferential equations and their systems.
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, Mayer brackets.
    3. Systems of equations and equations of higher order. Compatibility, power series solutions, convergence.
    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, solution methods for soliton equations.
Literature
    required literature
  • D. Hilbert a R. Courant. Methods of Mathematical Physics, Vol. 2. Wiley, 1989. info
    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
  • 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 (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The course comprises lectures and tutorials. To pass the course, the first step is to earn credit for tutorials by earning 70% on a written test.
The final exam comprises a written part and an oral part. The written part tests the ability to select and apply a suitable solution method. The written part is followed by the oral part, which tests the theoretical knowledge of the subject, including proofs.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (recent)
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