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EnglishIn 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 F; van der Mee C. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 127:1(2013), pp. 169-191.
| Titolo: | An alternative approach to integrable discrete nonlinear Schroedinger equations |
| Autori: | |
| Data di pubblicazione: | 2013 |
| Rivista: | |
| Citazione: | An alternative approach to integrable discrete nonlinear Schroedinger equations / Demontis F; van der Mee C. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 127:1(2013), pp. 169-191. |
| 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 |
| Handle: | http://hdl.handle.net/11584/104105 |
| Tipologia: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11584/104105
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