Elliptic Solitons in (1+2)-Dimensional Anisotropic Nonlocal Nonlinear Fractional Schrödinger Equation

Abstract

This paper obtains the numerical solutions of the elliptic solitons in a (1+2)dimensional anisotropic nonlocal nonlinear fractional Schrödinger equation, and verifies their stabilities by the direct propagation method. The results show that the properties of such solitons relatively depend on the Lévy index. Such as the soliton shape varies with the change of Lévy index. When the Lévy index decreases, the ellipticity will increase, while the critical power will decrease. Furthermore, we demonstrate the physical features exhibited by the higher order elliptic solitons for a different Lévy index.

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

“…However, its application to quantum mechanics was started by the pioneering work of the Laskin and others . Based on this outstanding idea, intense investigations have been carried out in different fields of studies, for example, energy band structure for the periodic potential, position‐dependent mass fractional Schrödinger equation, fractional quantum oscillator, nuclear dynamics of the H 2 + molecular ion, propagation dynamics of a light beam, spatial soliton propagation, solitons in the fractional Schrödinger equation with parity‐time‐symmetric lattice potential, gap solitons, Rabi oscillations in a fractional Schrödinger equation, self‐focusing, and wave collapse, elliptic solitons, light propagation in honeycomb lattice, and so on. These studies are based on the different methods such as domain decomposition method, energy conservative difference scheme, conservative finite element method, fractional Fan subequation method, split‐step Fourier spectral method, transfer‐matrix method, and so on.…”

Generation, dynamics and bifurcation of high power soliton beams in cubic-quintic nonlocal nonlinear media

“…Such CQNNL systems host solitons of versatile profiles. For example, a vortex soliton can be generated and stabilized in a (1 + 2) dimensional CQNNL system [15] or an elliptic soliton can be excited in an anisotropic (1 + 2) dimensional CQNNL system [16]. In contrast to the above investigations, we present a bright soliton formation in (1 + 1) dimensional CQNNL system.…”

Quantum tunneling from family of Cantor potentials in fractional quantum mechanics

“…The domain of SFQM have grown fast over the last two decades and various applications are discussed by different authors. Some of the notable work are the energy band structure for the periodic potential [6], position-dependent mass fractional Schrodinger equation [7], fractional quantum oscillator [8], nuclear dynamics of the H + 2 molecular ion [9], propagation dynamics of a light beam [10], spatial soliton propagation [11], solitons in the fractional Schrodinger equation with parity-time-symmetric lattice potential [12], gap solitons [13], Rabi oscillations in a fractional Schrodinger equation [14], self-focusing and wave collapse [15], elliptic solitons [16], light propagation in a honeycomb lattice [17], scattering features in non-Hermitian SFQM [18], tunneling time [19,20] etc. Different methods are used in such studies such as domain decomposition method [21], energy conservative difference scheme [22], conservative finite element method [23], fractional Fan sub-equation method [24], split-step Fourier spectral method [25], transfer-matrix method [26] etc.…”