Self-similar solitary wave family in Bessel lattice

Cai, Zebin; Jiang, Liang; Xia, Xiongping; Jiang, Yue; Jin, Hai-Qin; Yi, Lin

doi:10.1063/1.3589985

“…Other kinds of similarity transformations have been studied for nonautonomous NLSEs in various contexts. [5][6][7][8]16] Requiring Q to satisfy Eq. ( 2) and u to be a solution of Eq.…”

Section: Model and Nonautonomous Solitonsmentioning

confidence: 99%

“…For example, Serkin et al [4] paid their attention to the optical and matter-wave 3D nonautonomous soliton bullets. Cai et al [5] discussed the formation and propagation of self-similar solitary wave family in Kerr nonlinear media with external Bessel lattice. Beitia et al [6] and Dai et al [7] obtained periodic localized solutions by reducing (1+1)-dimensional and (2+1)dimensional NLSEs with spatially modulated parameters into the stationary NLSEs, respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonautonomous Solitons in the (3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

Liu¹,

Dai²

2012

Commun. Theor. Phys.

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We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrödinger equation in the (3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton's phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.

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“…More recently, Serkin et al [7] investigated the optical and matter-wave 3D nonautonomous soliton bullets. Cai et al [8] discussed the formation and propagation of self-similar solitary wave family in Kerr nonlinear media with external Bessel lattice. These nonautonomous solitons are governed by the nonautonomous NLSEs or Gross-Pitaevskii equations (GPEs).…”

Section: Introductionmentioning

confidence: 99%

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Haba¹,

Kaneta²,

Matsumoto³

et al. 2012

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A series of analytical nonautonomous soliton solutions for the (3+1)dimensional nonlinear Schrödinger equation with variable coefficients in the presence of gain (loss) and a harmonic potential are obtained. The explicit functions which describe the evolution of the amplitude, phase and velocity are also given. Soliton's phase and velocity are independent of the gain parameter, and only the amplitude is affected by the gain parameter. The dynamical behaviors for nonautonomous chirp-free and chirped solitons in a periodic distributed and dispersion decreasing systems are discussed. By modulating appropriate diffraction/dispersion parameters, we can trap the velocity of each soliton to control the interaction between soliton pairs. The real and imaginary parts of the spectral parameters control the separating or interacting behavior of chirp-free soliton pairs. However, the appearance of the chirp restrains the interaction between the chirped soliton pairs.

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“…More recently, Serkin et al [7] investigated the optical and matter-wave 3D nonautonomous soliton bullets. Cai et al [8] discussed the formation and propagation of self-similar solitary wave family in Kerr nonlinear media with external Bessel lattice. These nonautonomous solitons are governed by the nonautonomous NLSEs or Gross-Pitaevskii equations (GPEs).…”

Section: Introductionmentioning

confidence: 99%

Untitled

Dai¹,

Xu²

2012

Acta Phys. Pol. B

0

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A series of analytical nonautonomous soliton solutions for the (3+1)dimensional nonlinear Schrödinger equation with variable coefficients in the presence of gain (loss) and a harmonic potential are obtained. The explicit functions which describe the evolution of the amplitude, phase and velocity are also given. Soliton's phase and velocity are independent of the gain parameter, and only the amplitude is affected by the gain parameter. The dynamical behaviors for nonautonomous chirp-free and chirped solitons in a periodic distributed and dispersion decreasing systems are discussed. By modulating appropriate diffraction/dispersion parameters, we can trap the velocity of each soliton to control the interaction between soliton pairs. The real and imaginary parts of the spectral parameters control the separating or interacting behavior of chirp-free soliton pairs. However, the appearance of the chirp restrains the interaction between the chirped soliton pairs.

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Self-similar solitary wave family in Bessel lattice

Cited by 3 publications

References 30 publications

Nonautonomous Solitons in the (3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

Nonautonomous Solitons in the (3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

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