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Riemann surfaces and their applications in integrable system

Riemann surfaces and their applications in integrable system
1hr 59min of on-demand video
English
English [Auto]

Requirements

  • To understand this course, you need to know basic facts from the theory of function of complex variables and calculus

    Description

    This course will discuss the beautiful and fascinating object Riemann surfaces. Many applications of Riemann surfaces in integrable systems are possible. Our main goal is to show how Riemann surface and their degenerations within singular algebraic curves can be used to solve problems in geometry and integrable models mathematical physics. One example of such models is the Korteweg–de Vries equation.

    ut = (6 U uxx +uxxx)/4, u = (x, t).

    This equation describes solitons. They are solitary water waves within a channel. The theory of Riemann surface and its application in integrable models mathematical physics.

    Sincerely, Andrey Mirov.

    Opisanie kursa na russkom iazyke

    V etomkurse my obsuzhdaem, ochen’ interestnye and i krasivye. – Rimanovy poverkhnosti. Rimanovy poverkhnosti imeiut mnogo razlichnykh primenii v integriruemykh sistemakh. I odna iz nashikh glavnykh tselei ob’iasnit, kak rimanovy poverkhnosti i ikh vyrozhdeniia v singleuliarnykh algebraicheskikh krivykh pomogaiut reshat’ zadachi iz geometrii i integriruemykh fiziki Naprimer, Odnoi iz Takikh Modelei Iavliaetsia Uravnenie Kortevega–de Friza

    ut = (6 U uxx +uxxx)/4, u = (x, t).

    Eto uravnenie solitony to est’ odinochnye vody v Kanale.

    Teoriia rimanovykh poverkhnostei i ee prilozheniia v integriruemykh matematicheskoi fiziki. My budem rady videt’ Vas nashem Kurse!

    Priiatnogo izucheniia.

    Andrei Mironov, S uvazheniem

    Who this course is for:

    • Master’s students in geometry and mathematical physics.

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