Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations

Pelinovsky, Dmitry E.; Yang, Jianke

doi:10.1111/j.1467-9590.2005.01565

Cited by 45 publications

(42 citation statements)

References 39 publications

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“…In these cases the linearised operators b and c would be of zero order. In models of optical pulse propagation of birefringent fibres and in wavelength-divisionmultiplexed systems they are of the first order (see Pelinovsky and Yang [25]). They may be of higher orders as well, for example in models of optical solitons with higher order effects (see Nakkeeran [24]).…”

Section: This Is the Simplest Example Of Schrödinger Equations Couplementioning

confidence: 99%

Smoothing estimates for non-dispersive equations

Ruzhansky

Sugimoto

2015

Math. Ann.

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This paper describes an approach to global smoothing problems for non-dispersive equations based on ideas of comparison principle and canonical transformation established in authors' previous paper (Ruzhansky and Sugimoto, Proc Lond Math Soc, 105:393-423, 2012), where dispersive equations were treated. For operators a(D x ) of order m satisfying the dispersiveness condition ∇a(ξ ) = 0 for ξ = 0, the global smoothing estimateis well-known, while it is also known to fail for non-dispersive operators. For the case when the dispersiveness breaks, we suggest the estimate in the form

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Section: This Is the Simplest Example Of Schrödinger Equations Couplementioning

confidence: 99%

Smoothing estimates for non-dispersive equations

Ruzhansky

Sugimoto

2015

Math. Ann.

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“…Analytical study of this phenomenon demands a separate consideration and can be performed, for example, by a stability analysis as developed in Ref. [43]. Second, we have restricted ourselves to the study of the adiabatic approximation of the general perturbation theory.…”

Section: Discussionmentioning

confidence: 99%

“…Such a state can be treated as a pair of two ferromagnetic solitons with antiparallel spins [22]. Previous analysis of stability of multi-humped vector solitons for the cubic nonlinearity revealed that they are always unstable [42,43]. Hence, we can suggest that the most likely scenario of the polar soliton evolution under the action of a perturbation would be its splitting into a pair of ferromagnetic solitons.…”

Section: Soliton Solutions a Rank-one Solitonmentioning

confidence: 99%

Perturbation theory for bright spinor Bose-Einstein condensate solitons

2008

Self Cite

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We develop a perturbation theory for bright solitons of the F = 1 integrable spinor Bose-Einstein condensate (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferromagnetic rank-two soliton. Taking into account a splitting of a perturbed polar rank-two soliton into two ferromagnetic solitons, it is sufficient to elaborate a perturbation theory for the rank-one solitons only. Treating a small deviation from the integrability condition as a perturbation, we describe the spinor BEC soliton dynamics in the adiabatic approximation. It is shown that the soliton is quite robust against such a perturbation and preserves its velocity, amplitude, and population of different spin components, only the soliton frequency acquires a small shift. Results of numerical simulations agree well with the analytical predictions, demonstrating only slight soliton profile deformation.

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“…The coupled-NLS system with D 2 ¼ 1 may have multi-hump soliton solutions too, but they are expected to be unstable [25,26]. In this paper, we aim to demonstrate that, for values D 2 < 1, including small negative values of the relative GVD coefficient (i.e., the case of weak normal GVD in the v-component), Eqs.…”

Section: Introduction and The Modelmentioning

confidence: 96%

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

Chen

Malomed

2010

Optics Communications

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a b s t r a c tWe report results of the study of solitons in a system of two nonlinear-Schrödinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single-and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective ''management" scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.

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Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations

Cited by 45 publications

References 39 publications

Smoothing estimates for non-dispersive equations

Smoothing estimates for non-dispersive equations

Perturbation theory for bright spinor Bose-Einstein condensate solitons

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

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