Review of heavy-nucleus-acoustic nonlinear structures in cold degenerate plasmas

Sultana, S.

doi:10.1007/s41614-022-00067-3

Cited by 9 publications

(1 citation statement)

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“…The Nonlinear Schrödinger Equation (NLSE) is a nonlinear partial differential equation that describes the evolution of wave functions in quantum mechanics. It finds extensive applications across various fields of physics, including optics [1], cold atomic physics [2], and plasma physics [3]. In nonlinear optics, the NLSE serves as a fundamental mathematical model to depict the behavior of light waves in nonlinear media.…”

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%