Solitons for the cubic-quintic nonlinear Schrödinger equation with Raman effect in nonlinear optics

Wang, Ping; Shang, Tao; Li, Feng; Du, Yihong

doi:10.1007/s11082-013-9840-8

Cited by 17 publications

(10 citation statements)

References 23 publications

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“…(1), Ref. [23] presented bright one-and twosimilariton solutions for the constant-coefficient C-QNLS equation. Our general analytical approach, then, involves establishing a one-to-one correspondence between Eq.…”

Section: Ultrashort Nonautonomous Similariton Solutionsmentioning

confidence: 99%

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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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Section: Ultrashort Nonautonomous Similariton Solutionsmentioning

confidence: 99%

“…By substituting ansatz (2) into Eq. (1), one can arrive at a constant-coefficient C-QNLS equation which also possesses a Raman-shift term (this model is known as the Kundu-Eckhaus equation [20,23]) such that…”

Section: Bright Similariton Solutionsmentioning

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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“…(iii) The presence of higher-order derivative u 4t in the equation: (27) makes the Cauchy problem for this equation linearly ill-posed [43]. (iv) The solutions of the linear Equations (4) and (5) and the linear parts of Equations (6)- (8) contain decaying as well as growing modes of the form exp(±σz − iωt), as we shall see in Sections 3.2 and 3.3.…”

Section: Consequencementioning

confidence: 99%

“…(a) −iu ttt and/or u 4t : these higher-order derivatives are necessary to describe sub-picosecond pulses [1][2][3][4][5][6][7][8][9][10][11][12]; in particular, conditions for including u 4t and discarding −iu ttt are discussed in [7,9], (b) |u| 4 u: this higher-order nonlinearity is used when we want to describe the propagation of pulses when the light intensity approaches the values which produce the "saturation" of the refractive index [13][14][15][16][17][18][19][20], (c) i(|u| 2 u) t : this term is necessary to describe the self-steepening of the optical pulses [21][22][23], (d) u(|u| 2 ) t : this term is associated with the effect of Raman scattering [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

2017

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Abstract:We study linear and nonlinear pulse propagation models whose linear dispersion relations present bands of forbidden frequencies or forbidden wavenumbers. These bands are due to the interplay between higher-order dispersion and one of the terms (a second-order derivative with respect to the propagation direction) which appears when we abandon the slowly varying envelope approximation. We show that as a consequence of these forbidden bands, narrow pulses radiate in a novel and peculiar way. We also show that the nonlinear equations studied in this paper have exact soliton-like solutions of different forms, some of them being embedded solitons. The solutions obtained (of the linear as well as the nonlinear equations) are interesting since several arguments suggest that the Cauchy problems for these equations are ill-posed, and therefore the specification of the initial conditions is a delicate issue. It is also shown that some of these equations are related to elliptic curves, thus suggesting that these equations might be related to other fields where these curves appear, such as the theory of modular forms and Weierstrass ℘ functions, or the design of cryptographic protocols.

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“…The non-linear Schrödinger equation is a generalized (1+1)-dimensional version of the Ginzburg-Landau equation presented in 1950 in their study on supraconductivity and has been specifically reported by Chiao et al [1] in their research of optical beams. In the past several years, various methods have been proposed to obtain the exact optical soliton solutions of the non-linear Schrödinger equation [2][3][4][5][6][7][8][9][10][11][12]. Dispersion and non-linearity are two of the essential components for the distribution of solitons across inter-continental regions.…”

Section: Introductionmentioning

confidence: 99%

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

et al. 2020

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The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the non-linear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.

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Solitons for the cubic-quintic nonlinear Schrödinger equation with Raman effect in nonlinear optics

Cited by 17 publications

References 23 publications

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

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