Publisher's Note: Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients [Phys. Rev. A<b>78</b>, 023821 (2008)]

Zhong, Wei‐Ping; Xie, Rong; Belić, Milivoj R.; Petrović, Nikola; Chen, Goong

doi:10.1103/physreva.78.039906

Cited by 19 publications

(11 citation statements)

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“…In Eq. ( 2) we assume that u(x, y, t) = w(ξ, t) , ξ = x + q 2 (y, t) , (10) where q 2 = q 2 (y, t) is a function to be determined later. Substituting Eq.…”

Section: Reduction Of Ckpmentioning

confidence: 99%

Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

Zhang

Wang

2017

Commun. Theor. Phys.

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“…In Eq. ( 2) we assume that u(x, y, t) = w(ξ, t) , ξ = x + q 2 (y, t) , (10) where q 2 = q 2 (y, t) is a function to be determined later. Substituting Eq.…”

Section: Reduction Of Ckpmentioning

confidence: 99%

Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

Zhang

Wang

2017

Commun. Theor. Phys.

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“…Solitons in Kerr-type self-focusing media are governed by the cubic nonlinear Schrödinger (NLS) equation, and they are known to be unstable in two and three dimensions (2D and 3D) in homogeneous media, because of the collapse of the wave function. Various schemes to arrest the collapse were proposed, such as the use of weaker saturable [4,5] or quadratic nonlinearities [6][7][8], the application of the nonlinearity and/or GVD management [9], and the use of tandem structures, which are composed of periodically alternating linear dispersive and nonlinear layers [10].…”

Section: Introductionmentioning

confidence: 99%

Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient

et al. 2011

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We report approximate analytical solutions to the (3+1)-dimensional spatiotemporal nonlinear Schrödinger equation, with the uniform self-focusing nonlinearity, and a variable negative radial diffraction coefficient, in the form of three-dimensional solitons. The model may be realized in artificial optical media, such as left-handed materials and photonic crystals, with the anomalous sign of the group-velocity dispersion (GVD). The same setting may be realized through the interplay of the self-defocusing nonlinearity, normal GVD, and positive variable diffraction. The Hartree approximation is utilized to achieve a suitable separation of variables in the model. Then, an inverse procedure is introduced, with the aim to select a suitable profile of the modulated diffraction coefficient supporting desirable soliton solutions (such as dromions, single-and multi-layer rings, and multi-soliton clusters). The validity of the analytical approximation and stability of the solutions is tested by means of direct simulations.

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“…Rare experimental solutions have been provided in [15]. Zhong et al [16] gave exact spatial solitons for the (2 + 1)D NLSE by the F-expansion technique with the assumption of the ansatzs.…”

mentioning

confidence: 99%

“…Similarity transformation. -The propagation behavior of an optical beam in a Kerr-like bulk optical medium with varying diffraction, nonlinearity, and gain or loss can be expressed as the following (2 + 1)D generalized NLSE [16]:…”

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confidence: 99%

Exact spatial similaritons for the generalized (2+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

Dai¹,

Zhu²,

Wang³

et al. 2010

EPL

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Based on a similarity transformation, we obtain exact spatial bright and dark similariton pairs and bright similaritons on continuous-wave backgrounds of the generalized (2 + 1)-dimensional nonlinear Schrödinger equation with space-dependent diffraction, nonlinearity, and gain coefficients. Some characteristic examples with physical relevance and the interaction behaviors of these similaritons are studied.

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Publisher's Note: Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients [Phys. Rev. A78, 023821 (2008)]

Cited by 19 publications

References 0 publications

Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient

Exact spatial similaritons for the generalized (2+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

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