Inverse scattering problem for nonstationary Dirac-type system and some of its applications

Mansur I. Ismailov

Department of Mathematics, Gebze Technical University

Abstract: The inverse scattering problem (ISP) for a first-order nonstrict hyperbolic system (in the literature, this system is also called the nonstationary Dirac-type system) on the whole plane is considered. It is well known that every linear equation, which the ISP is effectively solved for, determines a class of nonlinear evolution equations that the inverse scattering transform (IST) method is suitable for its integration. By applying the Lax pair relation, a class of nonlinear evolution equations is obtained. Then the procedure of the IST method for the integration of this class is determined. In an exact solvable case of ISP, i.e. when the main equation of ISP (this equation is also called the Gelfand-Levitan-Marchenko type integral equation) is exactly solvable, class of nonlinear evolution equations can be solved explicitly by reducing it to the integral equation with degenerate kernel. The motivation of choosing the IST method is the effective solvability of the ISP for the linear equation which is related to the nonlinear equation by the Lax pair relation.

Yer : MSGSÜ Bomonti Binası, Fizik Bölümü
Tarih : 22 Kasım 2018 Perşembe, 15.00