Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices

Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder

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We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA and are unstable.

Original languageEnglish
Article number026604
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
StatePublished - 16 Feb 2012


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