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- W2024067576 abstract "We address the existence of traveling single-humped localized solutions in the spatially discrete nonlinear Schrödinger (NLS) equation. A mathematical technique is developed for analysis of persistence of these solutions from a certain limit in which the dispersion relation of linear waves contains a triple zero. The technique is based on using the Implicit Function Theorem for solution of an appropriate differential advance–delay equation in exponentially weighted spaces. The resulting Melnikov calculation relies on a number of assumptions on the spectrum of the linearization around the pulse, which are checked numerically. We apply the technique to the so-called Salerno model and the translationally invariant discrete NLS equation with a cubic nonlinearity. We show that the traveling solutions terminate in the Salerno model whereas they generally persist in the translationally invariant NLS lattice as a one-parameter family of solutions. These results are found to be in a close correspondence with numerical approximations of traveling solutions with zero radiation tails. Analysis of persistence also predicts the spectral stability of the one-parameter family of traveling solutions under time evolution of the discrete NLS equation." @default.
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- W2024067576 date "2007-12-01" @default.
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- W2024067576 title "One-parameter localized traveling waves in nonlinear Schrödinger lattices" @default.
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- W2024067576 doi "https://doi.org/10.1016/j.physd.2007.07.010" @default.
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