MU:MU25014 Solution Meth. for Nonlin. PDE - Course Information

MU25014 Solution Methods for Nonlinear Partial Differential Equations

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

• Geometry and Global Analysis (programme MU, N1101)

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.

• Enrolment Statistics (Summer 2019, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2019/MU25014