Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients

Cardoso, Wesley B.; Couto, Hugo L.C.; Avelar, A. T.; Bazeia, D.

doi:10.1016/j.cnsns.2017.01.012

Cited by 33 publications

(4 citation statements)

References 65 publications

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“…Due to its physical importance, this nonlinear wave evolution equation has been analyzed from different points of view. For instance, Cardoso et al have obtained the localized solutions for inhomogeneous quadratic-cubic NLS equation and studied their stability with respect to small random perturbations [22]. Triki et al have analyzed this equation with space and time modulated nonlinearities in presence of external potentials in the context of Bose-Einstein condensates [23].…”

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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Section: Introductionmentioning

confidence: 99%

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

Triki,

Kruglov

2022

Preprint

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“…The last decade has witnessed a highlight of the virtue of optical soliton solutions under the effects of nonlinear dispersion parameters, nonlinearity terms including normal/anomalous dispersion regime. Numerous works have been carried out to stress their importance in the quadratic-cubic (QC) type [1][2][3][4][5][6][7][8][9][10][11]. Very recently, some investigations have presented other optical soliton solutions obtained in a different context [12,13].…”

Section: Introductionmentioning

confidence: 99%

Coupled sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in magneto-optic waveguides with quadratic-cubic nonlinearity

Yomba¹

2022

Phys. Scr.

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The current paper is dedicated to the study of the propagation of progressive solitons in magneto-optical waveguides that carry the quartic-cubic nonlinearity described by a coupled system of of nonlinear Schrödinger equations. In this direction, we take the help of a modiﬁed F-expansion method which allows us to widen the class of solutions to these coupled equations and permit the propagation of diﬀerent waves in the two channels. First of all, we constructed the solutions in terms of Jacobi elliptic functions in the forms of dn−sn, dn−cn, and cn − sn. After that, we obtained the progressive soliton solutions when these functions approached their limiting values with regards to the modulus of ellipticity. The progressive solutions include bright-dark soliton, bright-bright soliton, dark-dark soliton, bright-front soliton, dark-front soliton. In addition, we present the Figures 1-6 which graphically exhibit the representative structures of each explicit solution for some special parameter values.

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“…Experimental work has been done to show the existence of bright solitons for attractive interactions (a < 0) [7] and dark solitons for repulsive interactions (a > 0) [8]. Authors have also studied the dynamics of BEC in the presence of competing cubic-quintic nonlinearity [9,10,11,12,13,14,15] and quadratic-cubic nonlinearity [16,17,18,19,20]. Over the past several years, there is a considerable interest on the existence of matter wave solutions for GP equation with time-dependent coefficients or generalized nonlinear Schrödinger equation (GNLSE) [21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Controlled self-similar matter waves in PT-symmetric waveguide

Pathania,

Kaur,

Goyal

et al. 2020

Preprint

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We study the dynamics of Bose-Einstein condensate coupled to a waveguide with parity-time symmetric potential in the presence of quadratic-cubic nonlinearity modelled by Gross-Pitaevskii equation with external source. We employ the self-similar technique to obtain matter wave solutions, such as bright, kinktype, rational dark and Lorentzian-type self-similar waves for this model. The dynamical behavior of self-similar matter waves can be controlled through variation of trapping potential, external source and nature of nonlinearities present in the system.

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Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients

Cited by 33 publications

References 65 publications

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

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

Coupled sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in magneto-optic waveguides with quadratic-cubic nonlinearity

Controlled self-similar matter waves in PT-symmetric waveguide

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