On 10 May seminar will be held online only.

Speaker: Mark Fels
Title: Variational/Symplectic and Hamiltonian Operators
Language: English
Zoom:
https://us06web.zoom.us/j/8817121842?pwd=bE5CckVhdTI5cXlTSGxUT3ZwV3BEdz09
Zoom Passcode: 1005

Abstract:

Given a differential equation (or system) \Delta = 0 the inverse problem
in the calculus of variations asks if there is a multiplier function Q
such that

  Q \Delta = E(L),

where E(L) = 0 is the Euler-Lagrange equation for a Lagrangian L. A
solution to this problem can be found in principle and expressed in
terms of invariants of the equation \Delta. The variational operator
problem asks the same question but Q can now be a differential operator
as the following simple example demonstrates for the evolution equation
u_t - u_{xxx} = 0,

D_x(u_t - u_{xxx}) = u_{tx} - u_{xxxx} = E(-1/2(u_t u_x + u_{xx}^2)).

Here D_x is a variational operator for u_t - u_{xxx} = 0.

This talk will discuss how the variational operator problem can be
solved in the case of scalar evolution equations and how variational
operators are related to symplectic and Hamiltonian operators.


The seminar meets on Wednesday evenings at 19:20 MSK in Zoom,
Meeting ID: 88 17 12 1842
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FROM 211.161.249.*