Compression and stretching of ring-vortex solitons in a bulk nonlinear medium

Lai, Xian-Jing; Cai, Xiao-ou; Zhang, Jie-Fang

doi:10.1088/1674-1056/24/7/070503

Cited by 8 publications

(4 citation statements)

References 28 publications

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“…Nonlinear evolution equations can be used to describe nonlinear phenomena and play a vital role in many fields [1][2][3][4]. Nonlinear science involves the related fields of natural sciences and social sciences, mainly including mathematics, medical chemistry, biology, astronomy, physics, economics and other important subject areas, which is to construct the connection between mathematics and other disciplines.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Zhang,

Bao

2024

Preprint

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In this article, we employ the Bell polynomial method to construct its bilinear form, bilinear Bäcklund transformation, Lax pair, the integrability, infinite conservation laws and superposition formula of the generalized (2 + 1)-dimensional variable-coefficient fifth-order KdV equation, which can help us get more properties, increase the diversity of solutions and get more new phenomenon. It applies the Lax pairs to test the complete integrability of the generalized (2 + 1) -dimensional variable-coefficient fifth-order KdV equation. According to the obtained bilinear Bäcklund transformation, infinite conservation laws and nonlinear superposition formula are derived. By using the nonlinear superposition formula of the solution, the double soliton solution is obtained from the single soliton solution of the equation. Utilizing a symbolic computation approach, we get the Lump solution and exponential of compound solution, breather-type solution and rouge wave solution with appropriate values of constant coefficients. The generalized (2 + 1)-dimensional variable - coefficient fifth-order KdV equation analyses the evolution of long waves with modest amplitudes propagating in plasma physics and the motion of waves in fluids and other mediums. Moreover, dusty plasma, oceanography, water engineering, and other nonlinear sciences.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Zhang,

Bao

2024

Preprint

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“…The interactions between optical solitons have always been attracting attention in the field of nonlinear optics since the interactions present lots of novel and fascinating phenomena such as soliton fusion, fission, and annihilation, as well as spiraling. [1][2][3][4][5][6][7][8] Wang et al investigated numerically the propagation and interactions of Airy-Gaussian beams in a cubicquintic nonlinear medium, and found that soliton pairs can be obtained by adjusting the phase shift and interval between two Airy-Gaussian beams. [9] Lan et al proposed a general propagation lattice Boltzmann model for a variable-coefficient compound Korteweg-de Vries-Burgers equation by selecting an equilibrium distribution function and adding a compensation function, and simulated the two-soliton solution by taking appropriate free parameters.…”

Section: Introductionmentioning

confidence: 99%

Generation and manipulation of bright spatial bound-soliton pairs under the diffusion effect in photovoltaic photorefractive crystals*

Zhang¹,

Zhao²,

Li³

et al. 2020

Chinese Phys. B

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The generation and propagation characteristics of bright spatial bound-soliton pairs (BSPs) are investigated under the diffusion effect in photovoltaic photorefractive crystals by numerical simulation. The results show that two coherent solitons, one as the signal light and the other as the control light, can form a BSP when the peak intensity of the control light is appropriately selected. Moreover, under the diffusion effect, the BSP experiences a self-bending process during propagating and the center of the BSP moves on a parabolic trajectory. Furthermore, the lateral shift of the BSP at the output face of the crystal can be manipulated by adjusting the peak intensity of the control light. The research results provide a method for the design of all-optical switching and routing based on the manipulation of the lateral position of BSPs.

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“…It is also relevant to refer to recent works addressing ring-and elliptic-shaped vortex solitons in relevant physical configurations. The compression and stretching of ring vortices in bulk nonlinear media have been recently investigated both analytically and numerically [64]. The existence and stability of vortex solitons in a ring-shaped partially parity-time-symmetric potential have been studied in detail, revealing that robust nonlinear vortices can be easily created by input Gaussian beams with embedded vorticities [65].…”

Section: Introductionmentioning

confidence: 99%

Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion

Lai

Qui

et al. 2018

Nonlinear Dyn

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By means of systematic simulations we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with embedded vorticity, in a dissipative medium modeled by the cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion (spatial-filtering) term, which is anisotropic in the transverse plane and periodically modulated in the longitudinal direction. We show the generation of stable square-and gear-shaped OVs, as well as tilted oval-shaped vortex rings, and string-shaped bound states built of a central fundamental soliton and two vortex satellites, or of three fundamental solitons. Their shape can be adjusted by tuning the strength and 2 modulation period of the inhomogeneous diffusion. Stability domains of the generated OVs are identified by varying the vorticity of the input and parameters of the inhomogeneous diffusion. The results suggest a method to generate new types of ring-shaped OVs with applications to the work with structured light. IntroductionIn the course of the past three decades, a great deal of interest was drawn to theoretical and experimental studies of the existence, stability, and excitation of localized patterns in optical and matter-wave media [1][2][3][4][5][6][7][8][9][10][11][12][13]. This work has produced many findings for temporal, spatial, and spatiotemporal solitons in both conservative and dissipative media, which offer applications to all-optical switching, pattern recognition, parallel data processing, and for guiding light by light. In particular, the cubic-quintic complex Ginzburg-Landau (CGL) equation [14,15] is a generic nonlinear model that predicts the generation of a plethora of temporal, spatial, and spatiotemporal patterns due to the simultaneous balance of gain and loss, and of self-focusing nonlinearity and either diffraction or dispersion (or both of them). The cubic-quintic CGL equation is an adequate model in diverse fields, such as superconductivity and superfluidity, fluid dynamics, reaction-diffusion phenomena, nonlinear photonics, matter waves (Bose-Einstein condensates), quantum field

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Compression and stretching of ring-vortex solitons in a bulk nonlinear medium

Abstract: Compression and stretching of ring-vortex solitons in a bulk nonlinear mediumLai Xian-Jing(来娴静) a)b) † , Cai Xiao-Ou(蔡晓鸥) b) , and Zhang Jie-Fang(张解放) a)c)

Cited by 8 publications

References 28 publications

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Generation and manipulation of bright spatial bound-soliton pairs under the diffusion effect in photovoltaic photorefractive crystals*

Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion

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