Algebraic bright and vortex solitons in self-defocusing media with spatially inhomogeneous nonlinearity

Wu, Yan; Xie, Qing; Zhong, Honghua; Wen, Liu; Wang, Hai

doi:10.1103/physreva.87.055801

Cited by 35 publications

(20 citation statements)

References 29 publications

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“…In recent different types of nonlinearities were discussed, including anti-Gaussian, exponential [7], and algebraic [8] nonlinearities. Subsequently, several other types of the SDF cubic nonlinearities have been shown to support stable bright solitons [9][10][11][12][13][14]. In addition, this interesting finding has been extended to diverse settings [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 85%

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

Xie

2014

Open Physics

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Abstract:We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable. PACS

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Section: Introductionmentioning

confidence: 85%

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

Xie

2014

Open Physics

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“…The formation of stable bright solitons requires diverging nonlinearities. Several different types of such nonlinearities have been discussed [10][11][12][13][14][15][16][17][18][19][20][21][22]. In certain situations, exact analytical results for bright soliton solutions have been obtained.…”

Section: Introductionmentioning

confidence: 96%

“…In certain situations, exact analytical results for bright soliton solutions have been obtained. In most of these previous works, spatially inhomogeneous SDF nonlinearities display a single-well structure, including antiGaussian [10,12,15,17,18], exponential [10,14,[20][21][22], and algebraic [11,16,22] nonlinearities.…”

Section: Introductionmentioning

confidence: 98%

Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity

Xie

Wang

et al. 2014

Phys. Rev. E

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We show that stable bright solitons can appear in a medium with spatially inhomogeneous self-defocusing (SDF) nonlinearity of a double-well structure. For a specific choice of the nonlinearity parameters, we obtain exact analytical solutions for the fundamental bright solitons. By making use of the linear stability analysis, the stability region in the parameter space for the exact fundamental bright soliton is obtained numerically. We also show the bifurcation from an antisymmetric to an asymmetric bright soliton for the SDF double-well nonlinearity.

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“…(3)) being a bright soliton: The stability of the soliton solution is analyzed here only for the case where α = 0, to ensure that the localized modulation profile (Eq. (6)) is not singular at |x| → ∞ (nevertheless, the self-defocusing singularity with α < 0 may readily support robust self-trapped modes [3][4][5][6][7][8][9][11][12][13]). In this situation, i.e., with α = 0 and m → 1, system (4) yields…”

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confidence: 99%

“…Modern fabrication technologies make it possible to create waveguides featuring spatially inhomogeneous nonlinearities that support novel classes of propagation patterns [2]. In particular, spatially inhomogeneous waveguides with a defocusing nonlinearity, whose local strength grows toward the periphery, can support diverse species of fundamental and higher-order solitons, including vortices, necklace rings, vortex gyroscopes, hopfions, and complex hybrid modes [3][4][5][6][7][8][9], as well as localized dark solitons [10]. Similar nonlinearity landscapes, featuring different growth rates of the local nonlinearity in opposite transverse directions, support strongly asymmetric bright solitons [11].…”

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confidence: 99%

Exact states in waveguides with periodically modulated nonlinearity

Ding¹,

Chan²,

Chow³

et al. 2017

EPL

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-We introduce a one-dimensional model based on the nonlinear Schrödinger/GrossPitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. Exact dark-bright soliton complex in a coupled system with a localized modulation structure is also briefly considered . The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.

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Algebraic bright and vortex solitons in self-defocusing media with spatially inhomogeneous nonlinearity

Cited by 35 publications

References 29 publications

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity

Exact states in waveguides with periodically modulated nonlinearity

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