Dark gap solitons in one-dimensional nonlinear periodic media with fourth-order dispersion

Li, Jiawei; Zhang, Yanpeng; Zeng, Jianhua

doi:10.1016/j.chaos.2022.111950

Cited by 7 publications

(4 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where x and z denote transverse and longitude spatial coordinates [42,43], respectively, and β represents the strength of fourth-order diffraction [62][63][64]. When β > 0, the fourthorder diffraction is normal, whereas it is anomalous when β < 0 [62][63][64]. The nonlinear refractive index change in the Kerr media δn(I) can be written as…”

Section: Physical Model and Basic Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Anomalous Interactions of Airy Solitons Modulated by a Fundamental Gaussian Beam and Fourth-Order Diffraction

Zhao,

Ge,

Shen

2023

Photonics

View full text Add to dashboard Cite

We investigate the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffraction and an in-phase (out-of-phase) Gaussian beam affect the interactions of solitons generated from Airy beams in unique ways. Different from previous results, suggesting that interactions of in-phase (out-of-phase) conventional beams are always attractive (repulsive), many anomalous interactions of Airy beams are obtained. Stable breathing Airy soliton pairs can be formed with fourth-order diffraction and a fundamental Gaussian beam.

show abstract

Section: Physical Model and Basic Equationsmentioning

confidence: 99%

“…Aside from quadratic diffraction, high-order diffraction should not be ignored [57]. For instance, fourth-order diffraction has deep impacts on nonlinear optics, e.g., the self-similar propagation of optical pulses [58], modulation instability [59], pure-quartic soliton lasers [60], and soliton states [61][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

Anomalous Interactions of Airy Solitons Modulated by a Fundamental Gaussian Beam and Fourth-Order Diffraction

Zhao,

Ge,

Shen

2023

Photonics

View full text Add to dashboard Cite

show abstract

“…Dark soliton dynamics, stability, interactions, phase dynamics, ultra-short dark soliton, vector dark solitons, their tunnelling effects etc in nonlinear lossless and lossy mediums are theoretically explored. [58][59][60][61][62][63][64][65] Relevant studies on the dark-bright vector soliton in fibre ring lasers [66], robust dark topological valley Hall edge soliton [67], dark soliton families in quintic nonlinear lattices [68], and dark gap solitons in nonlinear media with fourth-order dispersion [25,69] are reported recently. The dark gap soliton in Bose-Einstein codensates trapped by optical lattices is predicted both in defocusing cubic [70] and quintic [71] nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional PT -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

Thasneem¹,

Subha²

2023

Phys. Scr.

View full text Add to dashboard Cite

The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time (PT ) symmetric k-wave number Scarff-II potential have been analysed. We study the effect of the coefficient of the imaginary component of the PT-symmetric potential on the eigenvalue spectra of the ground and first excited states in linear and nonlinear models. Symmetric eigenmodes with real eigenvalues are obtained in the unbroken PT regime in both models. The linear stability analysis shows that the solutions are stable in the unbroken PT regime. The stable propagation of the solutions in linear and nonlinear media supported by PT-symmetric k-wave number Scarff-II potential is also investigated. The comparison of the solutions in the presence and the absence of nonlinearity reveals that in the self-defocusing Kerr medium nonlinearity suppresses the region of PT -symmetry. The influence of the width of the complex k-wave number Scarff-II potential and the depth of the real potential function on the PT-symmetry breaking have also been analysed.

show abstract

“…The nonlinear partial differential equation (PDE) arises in various areas, including nonlinear optics, chemical kinetics, geochemistry, optical fibers, solid-state physics, plasma physics, fluid mechanics, and fluid dynamics [1][2][3][4]. The importance of analytical solutions of the nonlinear PDEs lies in their ability to provide a deeper understanding of the underlying physics, offer insight into the behavior of complex systems, and serve as valuable tools for validating numerical methods [5]. Comparing numerical approximations with the known analytical solutions, researchers can assess the accuracy, convergence, and stability [6] of their numerical schemes.…”

Section: Introductionmentioning

confidence: 99%

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

CR,

Jang

2023

Preprint

View full text Add to dashboard Cite

This study comprehensively explores a unified methodology for deriving exact solutions to the fractional modified (3+1) dimensional Kudryashov-Sinelshchikov (KS) equation featuring variable coefficients. The fractional KS equation, which incorporates fractional local M-derivatives, presents a significant challenge because of its inherent nonlinearity and the introduction of spatially varying coefficients. Of paramount importance are these variable coefficients, as they introduce spatial dependence and intricately capture spatial variations within the equation. This complexity in spatial variation poses a formidable challenge in obtaining exact solutions. Our analytical examination offers profound insights into the intricate interplay between diverse variable coefficients and fractional parameters. This comprehensive analysis greatly enhances our capacity to interpret solutions across various scenarios, enriching our understanding of the nuanced behavior exhibited by the fractional Kudryashov-Sinelshchikov equation. Our investigation encompasses a diverse range of solution forms, including fractional, polynomial, exponential, and others. The outcomes of this study hold profound implications for an extensive array of scientific domains, spanning mathematical physics, fluid dynamics, and nonlinear optics. Furthermore, this research employs advanced data visualization techniques, comprising 3D plots, contour plots, and stream plots, to facilitate a deep comprehension of intricate physical phenomena. These visual aids concurrently illustrate how analytical solutions are influenced by varying conditions. Ams classification 2010: 45K05, 45G10, 83C15, 35Q35, 35Q68 , 35Q80

show abstract

Dark gap solitons in one-dimensional nonlinear periodic media with fourth-order dispersion

Cited by 7 publications

References 47 publications

Anomalous Interactions of Airy Solitons Modulated by a Fundamental Gaussian Beam and Fourth-Order Diffraction

Anomalous Interactions of Airy Solitons Modulated by a Fundamental Gaussian Beam and Fourth-Order Diffraction

One-dimensional PT -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

Contact Info

Product

Resources

About