Introduction to asymptotic analysis for integrable equations 1

Syllabus

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.

Annotation

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