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Introduction to asymptotic analysis for integrable equations 1 - NMMA569

Title:	Úvod do asymptotické analýzy pro integrovatelné rovnice 1
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Oleksandr Minakov, Ph.D.

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Pavel Pyrih, CSc. (14.06.2021)

Asymptotic analysis for different integrable equations in the case the initial data vanish at infinity. An elective course for master and graduate students.

Syllabus -

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (14.06.2021)

We will consider methods of asymptotic analysis for different integrable equations (Korteweg-de Vries equation, nonlinear Schrödinger equation, etc.) in the case when the initial data vanish at infinity.

Brief content: Lax pair representation for integrable equations, Jost solutions, Riemann-Hilbert problems, classical special functions (parabolic cylinder functions, Airy function, Bessel functions), steepest descent method for oscillatory Riemann-Hilbert problems.

Entry requirements -

Last update: doc. RNDr. Pavel Pyrih, CSc. (14.06.2021)

Students are supposed to be acquainted with complex analysis, ordinary differential equations and partial differential equations.