In this article we develop the direct and inverse scattering theory of a discrete matrix Zakharov-Shabat system with solutions U n and W n . Contrary to the discretization scheme enacted by Ablowitz and Ladik, a central difference scheme is applied to the positional derivative term in the matrix Zakharov-Shabat system to arrive at a different discrete linear system. The major effect of the new discretization is that we no longer need the following two conditions in theories based on the Ablowitz-Ladik discretization: (a) invertibility of I N −U n W n and I M −W n U n , and (b) I N −U n W n and I M −W n U n being nonzero multiples of the respective identity matrices I N and I M

An alternative approach to integrable discrete nonlinear Schroedinger equations

DEMONTIS, FRANCESCO;VAN DER MEE, CORNELIS VICTOR MARIA
2013

Abstract

In this article we develop the direct and inverse scattering theory of a discrete matrix Zakharov-Shabat system with solutions U n and W n . Contrary to the discretization scheme enacted by Ablowitz and Ladik, a central difference scheme is applied to the positional derivative term in the matrix Zakharov-Shabat system to arrive at a different discrete linear system. The major effect of the new discretization is that we no longer need the following two conditions in theories based on the Ablowitz-Ladik discretization: (a) invertibility of I N −U n W n and I M −W n U n , and (b) I N −U n W n and I M −W n U n being nonzero multiples of the respective identity matrices I N and I M
Inverse scattering transform Integrable discrete nonlinear Schroedinger equation Marchenko method
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/104105
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