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Controllable propagation of Pearcey–Gaussian beams in photorefractive media with fractional Schrödinger equation

Guo Teng, Gao Ru, Ren Shumin, Wang Pengxiang, Xiao Yan

Optica Applicata

2022

Vol. 52, nr 4

627--638

Taking the fractional Schrödinger equation as the theoretical model, the evolution behavior of the Pearcey–Gaussian beam in the photorefractive medium is studied. The results show that breathing solitons are generated when the nonlinear effect and the diffraction effect are balanced with each other. Nonlinear coefficients, Lévy index and beams amplitude affect breathing period of the soliton and maximum peak intensity. Within a certain range, the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. However when the beams amplitude increases, the breathing period and the maximum peak intensity of the soliton increase. Under the photorefractive effect, due to the bidirectional self-acceleration property of the Pearcey beam, the solitons formed will propagate vertically. These properties can be used to manipulate the beam and have potential applications in optical switching, plasma channeling, particle manipulation, etc.

Application of Residual Power Series Method for the Solution of Time-fractional Schrödinger Equations in One-dimensional Space

Arqub Omar Abu

Fundamenta Informaticae

2019

Vol. 166, nr 2

87--110

The object of this article is to present the computational solution of the time-fractional Schrödinger equation subject to given constraint condition based on the generalized Taylor series formula in the Caputo sense. The algorithm methodology is based on construct a multiple fractional power series solution in the form of a rabidly convergent series with minimum size of calculations using symbolic computation software. The proposed technique is fully compatible with the complexity of this problem and obtained results are highly encouraging. Efficacious computational experiments are provided to guarantee the procedure and to illustrate the theoretical statements of the present algorithm in order to show its potentiality, generality, and superiority for solving such fractional equation. Graphical results and numerical comparisons are presented and discussed quantitatively to illustrate the solution.

On Fractional Schrödinger Equation

Rozmej P., Bandrowski B.

Computational Methods in Science and Technology

2010

Vol. 16, No. 2

191-194

In the note, recent efforts to derive fractional quantum mechanics are recalled. Some applications of a fractional approach to the Schrödinger equation are discussed as well.