Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-12-19
Physica D 216 (2006) 77-89
Nonlinear Sciences
Pattern Formation and Solitons
To appear Physica D. 23 pages, 13 figures
Scientific paper
We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities. We produce a stability diagram for different families of soliton solutions, that suggests the (co)existence of infinitely many branches of stable localized solutions. Bifurcations which occur with the increase of the coupling constant are studied in a numerical form. A variational approximation is developed for accurate prediction of the most fundamental and next-order solitons together with their bifurcations. Salient properties of the model, which distinguish it from the well-known cubic DNLS equation, are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space. The asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations.
Carretero-González Ricardo
Chong Ching Chieng
Malomed Boris A.
Talley J. D.
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