Chirped self-similar waves for quadratic–cubic nonlinear Schrödinger equation

Pal, Ritu; Loomba, Shally; Kumar, C. N.

doi:10.1016/j.aop.2017.10.007

Cited by 35 publications

(10 citation statements)

References 48 publications

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“…The law first appeared in 2011 [22]. The model supports soliton solutions (both temporal and spatial) with applications in soliton lasers, optical communications, ultra fast soliton switches and logic gate devices [47]. Recently, we observe many new progresses in the field of c Vilnius University, 2019 nonlinear optics [2-15, 17-26, 28, 29, 31-46, 48-55, 57-60].…”

Section: Introductionmentioning

confidence: 68%

“…Recently, we observe many new progresses in the field of c Vilnius University, 2019 nonlinear optics [2-15, 17-26, 28, 29, 31-46, 48-55, 57-60]. The NLSE with quadraticcubic nonlinearity is given by [6,19,25,27,47,54]:…”

Section: Introductionmentioning

confidence: 99%

“…The chaotic phenomena of the equation was studied in [27]. In [47], the analytical self-similar wave solutions of the equation were constructed. In [54], the method of undetermined coefficients was adopted to extract the soliton solutions and the conservation laws of the equation were reported.…”

Section: Introductionmentioning

confidence: 99%

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Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

Aliyu

Yusuf

Băleanu

2018

NAMC

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This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.

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Section: Introductionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

Aliyu

Yusuf

Băleanu

2018

NAMC

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“…Such equation may be used as an approximate form of the GPE for quasi-one-dimensional Bose-Einstein condensate with contact repulsion and dipole-dipole attraction [20]. This model can be also applied for the description of light beam propagation in a non-centrosymmetric waveguide exhibiting second-and third-order nonlinearity [21]. Due to its physical importance, this nonlinear wave evolution equation has been analyzed from different points of view.…”

Section: Introductionmentioning

confidence: 99%

Novel solitary and periodic waves in quadratic-cubic non-centrosymmetric waveguides

Triki,

Kruglov

2022

Preprint

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We present a wide class of novel solitary and periodic waves in a non-centrosymmetric waveguide exhibiting second-and third-order nonlinearities. We show the existence of bright, gray, and Wshaped solitary waves as well as periodic waves for extended nonlinear Schrödinger equation with quadratic and cubic nonlinearities. We also obtained the exact analytical algebraic-type solitary waves of the governing equation, including bright and W-shaped waves. The results illustrate the propagation of potentially rich set of nonlinear structures through the optical waveguiding media. Such privileged waveforms characteristically exist due to a balance among diffraction, quadratic and cubic nonlinearities.

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“…These waves can preserve their overall shapes during propagation by adjusting their amplitudes and widths to accommodate gradual longitudinal variations in system parameters [1][2][3]. Much attention in the optics literature has been paid to similaritons in fiber lasers [3][4][5][6][7] and amplifiers [8,9], dispersion-decreasing fibers [10][11][12], and tapered inhomogeneous nonlinear waveguides [13][14][15][16][17][18]. Generic theoretical models governing the dynamics of similaritons tend to be based on the well-known nonlinear Schrödinger (NLS) equation [1,2].…”

Section: Introductionmentioning

confidence: 99%

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

Yang

Gao

Jia

et al. 2020

Optics Communications

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Similarity transformation and Hirota bilinearization are deployed to derive exact bright and dark ultrashort one-and two-similariton solutions of a nonautonomous cubic-quintic nonlinear Schrödinger equation. Such wave packets may emerge when group-velocity dispersion and cubic-quintic self-phase modulations are balanced by Raman self-frequency shift in the presence of an external harmonic trap and linear gain or loss. The solutions presented here can be used to investigate the compression, amplification and interaction phenomena associated with bright and dark similaritons in inhomogeneous fiber systems. Furthermore, the dynamics of the characteristic parameters of the similaritons are studied analytically, and similariton stability in a distributed system is tested through extensive computations. As an example application, the tunneling behavior of bright and dark similaritons through cascade dispersion barriers and dispersion wells on an exponential background is investigated, and some interesting novel features are uncovered which are expected to facilitate the control of bright and dark ultrashort similariton in experimental scenarios. Keywords two-similariton, interaction, Raman effect, harmonic potential, cascade tunneling () () () () () () () 0 zz z z w z z w z z p z z w z

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Chirped self-similar waves for quadratic–cubic nonlinear Schrödinger equation

Cited by 35 publications

References 48 publications

Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

Novel solitary and periodic waves in quadratic-cubic non-centrosymmetric waveguides

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

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