Stabilization of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Adhikari, Sadhan K.

doi:10.1103/physreve.71.016611

Cited by 29 publications

(10 citation statements)

References 32 publications

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“…Modulational instability (MI) induced by the interplay between nonlinearity and dispersion (in the temporal domain) or diffraction (in the spatial domain) is a generic phenomenon in nonlinear physics [1][2][3][4][5][6][7][8][9][10]. The slow modulation of a monochromatic plane wave in the system leads to exponential growth of the unstable modes and eventually may result in the formation of envelope soliton train.…”

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confidence: 99%

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

Xue

2012

Phys. Rev. E

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We consider the modulational instability (MI) of Bose-Einstein condensate (BEC) described by a modified Gross-Pitaevskii (GP) equation with higher-order nonlinearity both analytically and numerically. A new explicit time-dependent criterion for exciting the MI is obtained. It is shown that the higher-order term can either suppress or enhance the MI, which is interesting for control of the system instability. Importantly, we predict that with the help of the higher-order nonlinearity, the MI can also take place in a BEC with repulsively contact interactions. The analytical results are confirmed by direct numerical simulations.

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confidence: 99%

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

Xue

2012

Phys. Rev. E

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“…(5) with α(z) = 0 and the width w set equal to the variational solution obtained by solving Eq. (10). The convergence will be quick if the guess for the width w is close to the final width.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Light bullets were realized experimentally in arrays of wave guides [17]. There were many theoretical − numerical and analytical − studies which established robustness and approximate solitonic nature of the light bullets us- * adhikari@ift.unesp.br; URL: http://www.ift.unesp.br/users/adhikari ing the 3D nonlinear Schrödinger (NLS) equation [1] with a modified nonlinearity [7,8], dissipation [18], and/or dispersion [10]. A saturable nonlinearity leads to stable optical bullets [7].…”

Section: Introductionmentioning

confidence: 99%

“…The same is true about a two-dimensional (2D) spatial soliton with a Kerr nonlinearity. However, the solitons can be stabilized in higher dimensions for a saturable [6,7] or a modified nonlinearity [8], or by a nonlinearity [9] or dispersion [10] management among other possibilities [11,12]. A 2D spatiotemporal optical soliton has been observed [13] in a saturable nonlinearity generated by the cascading of quadratic nonlinear processes.…”

Section: Introductionmentioning

confidence: 99%

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Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

Adhikari

2016

Phys. Rev. E

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We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically. We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation.

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“…However, the spatiotemporal optical solitons with the temporally or spatially modulated parameters can be stabilized via the rapidly oscillating scattering length or dispersion coefficient in a Kerr medium [47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

et al. 2015

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Studied in this paper is a (3 + 1)-dimensional nonlinear Schrödinger equation with the group velocity dispersion, fiber gain-or-loss and nonlinearity coefficient functions, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber. With the Hirota method and symbolic computation, the bilinear form and dark multi-soliton solutions under certain variablecoefficient constraint are derived. Interactions between the different-type dark two solitons have been asymptotically analyzed and presented. Both velocities and amplitudes of the two linear-type dark solitons do not change before and after the interaction. The two parabolic-type dark solitons propagating with the opposite directions both change their directions after the interaction. Interaction between the two periodic-type dark solitons is also presented. Interactions between the linear-, parabolic-and periodic-type dark two solitons are elastic.

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Stabilization of a(3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Cited by 29 publications

References 32 publications

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

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