Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

Zhou, Qin; Zhu, Qiuping

doi:10.1080/09500340.2014.986549

Cited by 39 publications

(9 citation statements)

References 15 publications

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“…1999), variable parametric method (Zhang and Yi 2008), Darboux-Bäcklun transform, and the inverse scattering transform (Zhou et al. 2014) have been successfully applied to exactly solve these models. If one compares the solitary wave profile of the KdV equation presented in Fig.…”

Section: Numerical Applicationsmentioning

confidence: 99%

Calculation of eigenvalues of Sturm–Liouville equation for simulating hydrodynamic soliton generated by a piston wave maker

2016

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This paper focuses on the mathematical study of the existence of solitary gravity waves (solitons) and their characteristics (amplitude, velocity, ) generated by a piston wave maker lying upstream of a horizontal channel. The mathematical model requires both incompressibility condition, irrotational flow of no viscous fluid and Lagrange coordinates. By using both the inverse scattering method and a given initial potential we can transform the KdV equation into Sturm–Liouville spectral problem. The latter problem amounts to find negative discrete eigenvalues and associated eigenfunctions , where each calculated eigenvalue gives a soliton and the profile of the free surface. For solving this problem, we can use the Runge–Kutta method. For illustration, two examples of the wave maker movement are proposed. The numerical simulations show that the perturbation of wave maker with hyperbolic tangent displacement under physical conditions affect the number of solitons emitted.

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Section: Numerical Applicationsmentioning

confidence: 99%

Calculation of eigenvalues of Sturm–Liouville equation for simulating hydrodynamic soliton generated by a piston wave maker

2016

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“…Theoretical contributions to the development of the soliton theory have been made [4][5][6]. Due to the potential of optical solitons in the optical fiber transmission systems [7][8][9][10][11][12][13][14][15][16][17], attention has been paid to the NLS-type equations [18][19][20][21][22]. In order to study the NLS-type equations, methods have been proposed, such as the inverse scattering transformation [23], Bäcklund transformation [24][25][26] and Darboux transformation [27,28].…”

Section: Introductionmentioning

confidence: 99%

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

et al. 2015

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Studied in this paper is a (3 + 1)-dimensional nonlinear Schrödinger equation with the group velocity dispersion, fiber gain-or-loss and nonlinearity coefficient functions, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber. With the Hirota method and symbolic computation, the bilinear form and dark multi-soliton solutions under certain variablecoefficient constraint are derived. Interactions between the different-type dark two solitons have been asymptotically analyzed and presented. Both velocities and amplitudes of the two linear-type dark solitons do not change before and after the interaction. The two parabolic-type dark solitons propagating with the opposite directions both change their directions after the interaction. Interaction between the two periodic-type dark solitons is also presented. Interactions between the linear-, parabolic-and periodic-type dark two solitons are elastic.

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“…Our quick review shows that, up to now, the dynamics of laser solitons in different nonlinear fibers and optical materials, based on the use of NSE, modified by adding extra terms, is well studied [9][10][11][12][13][14][15][16][17][18] . However, exact analytical soliton solutions of GNAE are not found.…”

Section: Introductionmentioning

confidence: 99%

Higher order solitons in non-paraxial optics

Dakova

Slavchev²,

Dakova

et al. 2017

SPIE Proceedings

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The well-known (1+1D) nonlinear Schrödinger equation (NSE) governs the propagation of narrow-band pulses in optical fibers and others one-dimensional structures. For exploration the evolution of broad-band optical pulses (femtosecond and attosecond) it is necessary to use the more general nonlinear amplitude equation (GNAE) which differs from NSE with two additional non-paraxial terms. That is way, it is important to make clear the difference between the solutions of these two equations. We found a new analytical soliton solution of GNAE and compare it with the well-known NSE one. It is shown that for the fundamental soliton the main difference between the two solutions is in their phases. It appears that, this changes significantly the evolution of optical pulses in multisoliton regime of propagation and admits a behavior different from that of the higher-order NSE solitons.

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Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

Cited by 39 publications

References 15 publications

Calculation of eigenvalues of Sturm–Liouville equation for simulating hydrodynamic soliton generated by a piston wave maker

Calculation of eigenvalues of Sturm–Liouville equation for simulating hydrodynamic soliton generated by a piston wave maker

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

Higher order solitons in non-paraxial optics

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