Introduction to asymptotic analysis for integrable equations 2

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 are step-like.

Brief content: Elliptic and hyperelliptic surfaces, theta-functions, Baker-Akhiezer function,finite-gap potentials, nonlinear special functions (Painlevé transcendents).

Annotation

Asymptotic analysis for different integrable equations in the case the initial data are step-like. An elective course for master and graduate students.