Black optical solitons for media with parabolic nonlinearity law in the presence of fourth order dispersion

Palacios, S. L.; Fernández‐Díaz, J. M.

doi:10.1016/s0030-4018(00)00666-0

Cited by 109 publications

(45 citation statements)

References 20 publications

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“…(5) [33,34,35]. This equation has exact bright (i.e., A sech(kx)e it ) and dark (i.e., A tanh(kx)e it ) soliton solutions for certain sets of parameters [34,35,36].…”

Section: Dark Type Solitonmentioning

confidence: 99%

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Exact localized solutions of quintic discrete nonlinear Schrödinger equation

2003

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We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φ n+1 + φ n−1 = F (φ n ). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

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“…(5) [33,34,35]. This equation has exact bright (i.e., A sech(kx)e it ) and dark (i.e., A tanh(kx)e it ) soliton solutions for certain sets of parameters [34,35,36].…”

Section: Dark Type Solitonmentioning

confidence: 99%

“…The existence of exact localized solutions originates from the balance between quintic nonlinear term and 4th-order derivative term. This equation appears in the optical fiber transmission studies [34,35,37].…”

Section: Dark Type Solitonmentioning

confidence: 99%

Exact localized solutions of quintic discrete nonlinear Schrödinger equation

2003

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“…This equation is completely integrable by the inverse scattering transform [7]. This means that it is possible to find both solitary wave and multi-soliton solutions [8]. However, as one increases the intensity of the incident light power to produce shorter (femtosecond) pulses, non-Kerr nonlinearity effects become important and the dynamics of pulses should be described by the NLS family of equations with higher order nonlinear terms [9].…”

Section: Introductionmentioning

confidence: 99%

Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities

Triki

Biswas

2011

Math. Meth. Appl. Sci.

108

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Communicated by S. GeorgievThe dynamics of dark solitons is studied within the framework of a generalized nonlinear Schrödinger equation. The specific cases of parabolic law and dual-power law nonlinearity are considered. The solitary wave ansatz method is used to carry out the integration. All the physical parameters in the soliton solutions are obtained as functions of the dependent model coefficients. Parametric conditions for the existence of envelope solitons are given.

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“…The nonlinear Schrödinger's equation (NLSE) plays a vital role in various areas of Physics, Applied Mathematics and Biochemistry [1][2][3][4][5][6][7][8][9][10]. It appears in the study of Nonlinear Fiber Optics, Plasma Physics, Fluid Dynamics and in α-helix proteins in Biochemistry [2] just to mention a few.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a particular kind of solitons, called topological solitons, is going to be studied in the context of NLSE with fourth order dispersion (4OD). These topological solitons for the NLSE is particularly studied in the area of Nonlinear Optics in the context of dark optical solitons [6]. The NLSE with 4OD is going to be studied with Kerr and power law nonlinearity [9].…”

Section: Introductionmentioning

confidence: 99%