Multipole vector solitons in coupled nonlinear Schrödinger equation with saturable nonlinearity

温嘉美,; 薄文博,; 温学坤,; 戴朝卿,

doi:10.7498/aps.72.20222284

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…The NLSE is crucial in studying the nonlinear dynamics of semiconductor lasers, particularly in mode-locking and the generation of ultra-short optical pulses [5]. Moreover, it has wide-ranging applications in all-optical communications and all-optical information storage [6]. In recent years, many scholars have introduced fractional-order derivatives into the NLSE, leading to the fractional nonlinear Schrödinger equation (fNLSE).…”

Section: Introductionmentioning

confidence: 99%

The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

Wang,

Peng,

Cao

et al. 2024

Mathematics

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This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution.

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Section: Introductionmentioning

confidence: 99%

The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

Wang,

Peng,

Cao

et al. 2024

Mathematics

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Prediction of multipole vector solitons and model parameters for coupled saturable nonlinear Schrödinger equations

Jiang,

Si,

Dai

et al. 2024

Chaos, Solitons & Fractals

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Transmission and control of band gap vortex solitons in fractional-order diffraction honeycomb lattices

Wang,

Wei,

Liu

et al. 2024

Acta Phys. Sin.

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In this paper, the existence and transmission characteristics of gap vortex optical solitons in a honeycomb lattice are investigated based on the fractional nonlinear Schrödinger equation. Firstly, the band-gap structure of honeycomb lattice is obtained by the plane wave expansion method. Then the gap vortex solitons modes and their transmission properties in the fractional nonlinear Schrödinger equation with the honeycomb lattice potential are investigated through the modified squared-operator method, the split-step Fourier method and the Fourier collocation method, respectively. The results show that the transmission of gap vortex solitons are influenced by the lévy index and the propagation constant. The stable transmission region of gap vortex soliton can be obtained through power graphs. In the stable region, the gap vortex soliton can transmit stably without disturbance. However, in the unstable region, the gap vortex soliton will gradually lose ring structure and converge into a fundamental soliton as the transmission distance increasing. And the larger lévy index and the larger propagation constant, the stable transmission distance of gap vortex solitons will increase. When multiple vortex solitons transmit in the lattice, the interaction between them is influenced by the lattice position and phase. Two vortex solitons with in phase located at adjacent lattices are superimposed with sidelobe energy, while two vortex solitons with out of phase are cancelled with sidelobe energy. These vortex solitons will gradually lose ring structure and evolve into dipole modes during the transmission process. And they are periodic rotation under the azimuth angle modulating. When two vortex solitons located at non-adjacent lattice, vortex solitons can maintain a ring-shaped structure due to the small influence of sidelobes. When three gap vortex solitons are located at non-adjacent lattices, the solitons can also remain ring structure. However, when there are more than three gap vortex solitons, the intensity distribution of vortex solitons are uneven due to the sidelobe energy superimposed. These vortex solitons will form dipole modes and rotate under the azimuth angle modulating during transmission process. These results can offer theoretical guidance for the transmission and control of gap vortex solitons in the lattice.

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Multipole vector solitons in coupled nonlinear Schrödinger equation with saturable nonlinearity

Cited by 3 publications

References 23 publications

The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

Prediction of multipole vector solitons and model parameters for coupled saturable nonlinear Schrödinger equations

Transmission and control of band gap vortex solitons in fractional-order diffraction honeycomb lattices

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