Multistable solitons in the cubic–quintic discrete nonlinear Schrödinger equation

Carretero-González, R.; Talley, J.D.; Chong, Christopher; Malomed, Boris A.

doi:10.1016/j.physd.2006.01.022

Cited by 101 publications

(94 citation statements)

References 51 publications

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“…Very recently, similar predictions have been made for other nonlinear media, for example in cubic-quintic systems [26] and for localized surface waves [27].…”

supporting

confidence: 67%

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

et al. 2006

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We report on the formation of dark discrete solitons in a nonlinear periodic system consisting of evanescently-coupled channel waveguides that are fabricated in defocusing lithium niobate. Localized nonlinear dark modes displaying a phase jump in the center that is located either on-channel (mode A) or in-between channels (mode B) are formed, which is to our knowledge the first experimental observation of mode B. By numerical simulations we find that the saturable nature of the nonlinearity is responsible for the improved stability of mode B. The ability of the induced refractive index structures to guide light of a low-power probe beam is demonstrated.

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“…Very recently, similar predictions have been made for other nonlinear media, for example in cubic-quintic systems [26] and for localized surface waves [27].…”

supporting

confidence: 67%

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

et al. 2006

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“…12(b) features a loop, which is a characteristic feature of the SSB in models with saturable [22] and CQ nonlinearities. In the latter context, closed bifurcation loops were found in the discrete (lattice) version of the CQ model [31], and in a system of two linearly coupled NLS equations with the CQ nonlinearity [32]. The presence of the bifurcation loop implies that the broken symmetry is eventually restored, under the action of the quintic term.…”

Section: A Strong Couplingmentioning

confidence: 99%

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

Birnbaum

Malomed

2008

Physica D: Nonlinear Phenomena

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We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are symmetric and antisymmetric solitons of "broad" and "narrow" types, composite states, built as combinations of broad and narrow beams with identical or opposite signs ("unipolar" and "bipolar" states, respectively), and "single-sided" broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via eigenvalues of small perturbations, and is verified in direct simulations. Three species -narrow symmetric, broad antisymmetric, and unipolar composite states -are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak inter-channel coupling.

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“…Recently, localized states in this one-dimensional discrete model with the competing nonlinearities were studied in detail in Ref. [13], where it was shown that novel classes of solutions can be introduced by this competition.…”

Section: Introductionmentioning

confidence: 99%

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

Cuevas¹,

Kevrekidis

Frantzeskakis

et al. 2009

Physica D: Nonlinear Phenomena

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We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u| 2σ u. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ + 1 < 3.68; bistability, in a finite range of values of the soliton's power, for 3.68 < 2σ + 1 < 5, and the presence of a threshold (minimum norm of the FS), for 2σ + 1 ≥ 5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons, and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.

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Multistable solitons in the cubic–quintic discrete nonlinear Schrödinger equation

Cited by 101 publications

References 51 publications

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

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