Inverse scattering transform for the nonlinear Schrödinger system on a zigzag-runged ladder lattice
A detailed description of four-component nonlinear Schrödinger system on zigzag-runged ladder lattice is given. In order to support the equivalence between the two pairs of field amplitudes, we introduce the two sets of auxiliary linear problems, allowing one to develop the inverse scattering techni...
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Veröffentlicht in: | Journal of mathematical physics 2010-10, Vol.51 (10), p.103518-103518-45 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A detailed description of four-component nonlinear Schrödinger system on zigzag-runged ladder lattice is given. In order to support the equivalence between the two pairs of field amplitudes, we introduce the two sets of auxiliary linear problems, allowing one to develop the inverse scattering technique in the most adequate symmetrical form. The two complementary sets of discrete Marchenko equations are derived and their multisoliton solutions for the true reflectionless field amplitudes are found. The dispersion relations for the diagonal elements of reduced monodromy matrices are obtained. We explicitly present the simplest realization of soliton dynamics corresponding to the time-independent intersite coupling parameters and zero Peierls phases and show that the two-site structure of the lattice unit cell is strictly manifested as the two splitted branches of soliton excitations. In the general case of time-dependent intersite coupling parameters and nonzero Peierls phases, the theory is capable to model the dynamics of parametrically driven nonlinear ladder systems subjected to external magnetic field. |
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ISSN: | 0022-2488 1089-7658 |
DOI: | 10.1063/1.3481565 |