Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2009-07-08
Nonlinear Sciences
Pattern Formation and Solitons
4 pages, 4 figures
Scientific paper
We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schrodinger (NLS) model. We use singularity confinement techniques to suggest that the relevant discretization should not be integrable. More importantly, we identify the prototypical solitary waves of the model and examine their stability, illustrating the remarkable feature that near the continuum limit, this discretization leads to the absence of collapse and complete spectral wave stability, in stark contrast to the standard discretization of the NLS. We also briefly touch upon the three-dimensional case and generalizations of our considerations therein, and also present some more exotic solutions of the model, such as exact line solitons and discrete vortices.
Herring G. J.
Hoq Q. E.
Kevrekidis Panagiotis G.
Lafortune Stephane
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