[Free] Riemann Surfaces And Their Applications In Integrable System
– Free Course
What you’ll learn
- The theory of Riemann surfaces and its applications in integrable models of mathematical physics.
Requirements
- To understand this course, you need to know basic facts from the theory of function of complex variables and calculus
Description
In this course we discuss very interesting and beautiful object – Riemann surfaces. Riemann surfaces have many different applications in integrable systems. And one of our main aim is to explain how Riemann surfaces and their degenerations in singular algebraic curves help to solve problems from geometry and integrable models of mathematical physics. For example, one of such models is a famous Korteweg-de Vries equation:ut = (6 u uxx +uxxx )/4, u = u(x, t).
This equation describes solitons, that is, solitary water waves in a channel. The theory of Riemann surfaces and its applications in integrable models of mathematical physics.
Sincerely, Andrey Mironov.
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ut = (6 u uxx +uxxx )/4, u = u(x, t).
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Author(s): Andrey Mironov
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