Asymptotic analysis of integrable nonlinear partial differential equations by M. Filipkovska
On July 28th. our postdoctoral researcher Maria Filipkovska will talk on “Asymptotic analysis of integrable nonlinear partial differential equations” at the Guest Colloquium organized by the Women’s Representative of the Faculty of Natural Sciences at Friedrich-Alexander-Universität Erlangen-Nürnberg.
Abstract. We consider an approach to studying asymptotic behavior of solutions of initial-boundary value problems (IBVPs) for integrable nonlinear PDEs on the example of the system of the Maxwell-Bloch equations. Using the considered approach, we carry out asymptotic analysis of the Maxwell-Bloch (MB) equations. These equations, in particular, describe the propagation of electromagnetic wave in a resonant medium with distributed two-level atoms and arise in the problems of self-induced transparency, a two-level laser amplifier and superfluorescence. The inverse scattering transform method in the form of the matrix Riemann-Hilbert (RH) problem for the system of the MB equations is developed. This allows one to obtain a solution for the MB equations in terms of the solution of the associated RH problem. Finally, we represent explicit formulas for the asymptotics of a solution of an IBVP for the MB equations in different sectors of the space-time plane.
Zoom meeting link
Meeting ID: 645 0218 3255 | PIN: 555331
Room H13. Department of Mathematik.
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Cauestrasse 11, 91058 Erlangen