Seminar talk, 10 May 2023
Speaker: Mark Fels
Title: Variational/Symplectic and Hamiltonian Operators
Given a differential equation (or system) = 0 the inverse problem in the calculus of variations asks if there is a multiplier function such that
where is the Euler-Lagrange equation for a Lagrangian . A solution to this problem can be found in principle and expressed in terms of invariants of the equation . The variational operator problem asks the same question but can now be a differential operator as the following simple example demonstrates for the evolution equation ,
Here is a variational operator for .
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.