Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2009-01-19
Phys. Lett. A (2009), doi:10.1016/j.physleta.2009.07.082
Nonlinear Sciences
Pattern Formation and Solitons
16 pages, An important comment on the staggering transformation is now included
Scientific paper
10.1016/j.physleta.2009.07.082
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves is a signature of the modulation instability is used to analytically study instability effects on solitons during propagation. In particular, we concern with instability effects in the dark region, where other analytical methods as the standard modulation analysis of planewaves do not provide any information on solitons. The region of high-velocity solitons is studied anew showing that solitons are less prone to intabilities in this region. An analytical upper boundary for the self-defocusing instability is defined.
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