We investigated three-dimensional quantum systems with higher-order dispersion and nonlinear effects. The systems’ soliton dynamics is studied based on the (3+1)-dimensional higher-order nonlinear Schrödinger equation (NLSE). Based on the self-similar approach and the bright soliton-type solution of the (1+1)-dimensional NLSE, we derived the analytical bright soliton solution for the (3+1)-dimensional NLSE with higher-order dispersion and nonlinear effects, with the typical soliton feature pictorially demonstrated. Our study illustrates that a higher-dimensional medium with higher-order dispersion and nonlinear effects supports soliton behavior. This demonstrates the applicability of the theoretical treatment presented in this work.
In this paper, partially coherent radially polarized (RP) Laguerre–Gaussian (LG) rotationally symmetrical power–exponent phase vortex (RSPEPV) beams with the LG–correlated Schell–model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards–Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight–focusing properties of RP–LG–RSPEPV beams with LGSM and the order of LGSM p’, topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers.
In this work, we investigated one-dimensional and two-dimensional quantum systems with higher-order dispersions and higher-order nonlinear interactions. Based on the high-order nonlinear Schrödinger equation (NLSE) and via the [Formula: see text]-expansion method, we derived the analytical dark soliton solution for the one-dimensional system first. By applying the self-similar method and using the results of the one-dimensional case, the analytical dark soliton solution of the system in the two-dimensional case was derived. The dynamic evolution pattern of the two-dimensional dark soliton is pictorially demonstrated. The theoretical results of our work can be used to guide the detection and experimental study of dark soliton in a two-dimensional quantum system, using high-order dispersion and higher-order nonlinear interactions.
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