BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mark Fels DTSTART:20230510T162000Z DTEND:20230510T180000Z DTSTAMP:20260423T023042Z UID:GDEq/88 DESCRIPTION:Title: Va riational/Symplectic and Hamiltonian Operators\nby Mark Fels as part o f Geometry of differential equations seminar\n\n\nAbstract\nGiven a differ ential equation (or system) $\\Delta$ = 0 the inverse problem in the calcu lus of variations asks if there is a multiplier function $Q$ such that\n\\ [Q\\Delta=E(L)\,\\]\nwhere $E(L)=0$ is the Euler-Lagrange equation for a L agrangian $L$. A solution to this problem can be found in principle and ex pressed 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 eq uation $u_t - u_{xxx} = 0$\,\n\\[D_x(u_t - u_{xxx}) = u_{tx}-u_{xxxx}=E(-\ \frac12(u_tu_x+u_{xx}^2)).\\]\nHere $D_x$ is a variational operator for $u _t - u_{xxx} = 0$.\n\nThis talk will discuss how the variational operator problem can be solved in the case of scalar evolution equations and how va riational operators are related to symplectic and Hamiltonian operators.\n LOCATION:https://researchseminars.org/talk/GDEq/88/ END:VEVENT END:VCALENDAR