Seminar on nonlinear problems of PDE and mathematical physics on topic: “The Korteweg-de Vries equation on the Uhlenbeck manifold”
Seminar on nonlinear problems of PDE and mathematical physics on topic: “The Korteweg-de Vries equation on the Uhlenbeck manifold”
2023 The event passed
21 Feb
Location
Online
About the event
21 February at 19.00 (Moscow time)
Speakers: Professor Dymarsky Y. M. (Moscow Institute of Physics and Technology)
Title of the talk: The Korteweg-de Vries equation on the Uhlenbeck manifold
Annotation: It is known that the KdV equation with respect to the function p=p(x,t), periodic in the variable x, can be understood as a vector field v(p)=-p’’’ + 6pp’. It is also known that the solution p(x,t) of the KdV equation and the corresponding eigenfunction y(x,t) of the Schrödinger operator with the potential p(x,t) are related by the equation \dot{y} = −4y’’’+ 6 p(x,t) y’ + 3 p’(x,t). We will show that this equation can be understood as a vector field on the Karen Uhlenbeck manifold of triples (p,\lamda,y) satisfying the Schrödinger equation.
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