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arXiv · 1809.10828

Standing lattice solitons in the discrete NLS equation with saturation

G. L. Alfimov·A. S. Korobeinikov·C. J. Lustri·D. E. Pelinovsky
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Abstract

We consider standing lattice solitons for discrete nonlinear Schrodinger equation with saturation (NLSS), where so-called transparent points were recently discovered. These transparent points are the values of the governing parameter (e.g., the lattice spacing) for which the Peierls-Nabarro barrier vanishes. In order to explain the existence of transparent points, we study a solitary wave solution in the continuous NLSS and analyse the singularities of its analytic continuation in the complex plane. The existence of a quadruplet of logarithmic singularities nearest to the real axis is proven and applied to two settings: (i) the fourth-order differential equation arising as the next-order continuum approximation of the discrete NLSS and (ii) the advance-delay version of the discrete NLSS.

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G. L. Alfimov, A. S. Korobeinikov, C. J. Lustri, D. E. Pelinovsky. 2018-09-28. Standing lattice solitons in the discrete NLS equation with saturation. https://doi.org/10.1088/1361-6544%2Fab1294

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