Si-Liu Xu

Three-dimensional spatiotemporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients

We introduce three-dimensional (3D) spatiotemporal vector solitary waves in coupled (3+1)D nonlinear Schrodinger equations with variable diffraction and nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing for novel localized solutions. Using the Hirota bilinear method, 3D approximate but analytical spatiotemporal vector solitary waves are built with the help of spherical harmonics, including multipole solutions and necklace rings. Variable diffraction and nonlinearity allow utilization of soliton management methods. The comparison with numerical solutions is provided and the behavior of relative error is displayed. It is demonstrated that the spatiotemporal soliton profiles found are stable in propagation.

Light bullets in spatially modulated Laguerre–Gauss optical lattices

We investigate the generation and stability of light bullets (LBs) in Laguerre–Gauss (LG) optical lattices, in which both linear and nonlinear changes in the refractive index are spatially modulated. We demonstrate that the linear and nonlinear contributions considerably affect the bullet shape and its range of stability; at the same time the nonlinear modulation depth, through the propagation constant, affects the width of the stability domain. We find that the energy of stable space-time solitons increases with the increase in the modulation depth. We discover that the behavior of LBs in LG optical lattices is substantially different from the behavior in the more familiar Bessel lattices.

Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential

We construct exact self-similar soliton solutions of three-dimensional coupled Gross–Pitaevskii equations for two-species Bose–Einstein condensates (BECs) in a combined time-dependent harmonic-lattice potential. Based on these solutions, we investigate the control and manipulation of solitary waves for three kinds of BECs with changing diffraction and nonlinearity coefficients; the solutions include Ma breathers and Peregrine and Akhmediev soliton solutions. Our results indicate that matter waves readily propagate in this system. It is shown that diffraction and lattice potential factors play important roles in the beam evolution characteristics, such as the peak, the phase offset, the linear phase, and the chirp.

Vortex solitons in the (2 + 1)-dimensional nonlinear Schrödinger equation with variable diffraction and nonlinearity coefficients

Using Hirotas bilinear method, we determine approximate analytical localized solutions of the (2 + 1)-dimensional nonlinear Schrodinger equation with variable diffraction and nonlinearity coefficients. Our results indicate that a new family of vortices can be formed in the Kerr nonlinear media in the cylindrical geometry. Variable diffraction and nonlinearity coefficients allow utilization of the soliton management method. We present solitary solutions for two types of distributed coefficients: trigonometric and exponential. It is demonstrated that the soliton profiles found are structurally stable, but slowly expanding with propagation.

Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

Light bullets in three-dimensional complex Ginzburg-Landau equation with modulated Kummer-Gauss photonic lattice

We investigate the existence of spatiotemporal necklace vortex solitons or light bullets in the complex Ginzburg-Landau equation with the modulated Kummer-Gauss (KG) external lattice potential and the spiraling phase of vorticities , and 2. We find localized vortex necklaces in a three-dimensional nonlinear medium, trapped by the KG external potential with different orders of vorticity. Stable and quasi-stable solitons form from input pulses with embedded vorticity. The stability is established by calculating growth rates of the perturbed eigenmodes. We establish that spatiotemporal necklace solitons may coexist in a large domain of the parameter space.

Spatiotemporal soliton supported by parity-time symmetric potential with competing nonlinearities

We construct explicit spatiotemporal or light bullet (LB) solutions to the (3 + 1)-dimensional nonlinear Schrodinger equation (NLSE) with inhomogeneous diffraction/dispersion and nonlinearity in the presence of parity-time (PT) symmetric potential with competing nonlinearities. The solution is based on the similarity transformation, by which the initial inhomogeneous problem is reduced to the standard NLSE with constant coefficients but with redefined variables and potential. Transmission characteristics of LB solutions, such as the phase change, half width and chirp, are studied in the media with exponentially decreasing diffraction/dispersion and with periodic modulation. Our outcomes demonstrate that diffraction/dispersion and nonlinearity management can prolong the stability of LBs in a PT potential.

Light bullets in coupled nonlinear Schrödinger equations with spatially modulated coefficients and Bessel trapping potential

We discuss three-dimensional (3D) light bullets (LBs) in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity coefficients, under the action of a Bessel trapping potential. Exact spatiotemporal vector solitary waves, or LBs, are obtained using the method of separation of variables and the Hirota’s bilinear method. An inverse solution procedure is introduced, in which the desired localized solutions of equations are proposed first and then the corresponding diffraction and nonlinearity coefficients determined. New 3D wave packets are built with the help of spherical harmonics in the form of multipole, necklace, and toroidal solitary pulses. Numerical solution of the full system of equations indicates that an initial wave in the form of such 3D wave packets is longlived but slowly changing along the propagation direction.

Vortex solitons produced in spatially modulated linear and nonlinear refractive index waveguides

We discuss analytical localized soliton solutions to the generalized nonautonomous nonlinear Schrodinger equation (NLSE) in waveguides featuring transverse modulation of both the linear and nonlinear refractive index changes. We utilize the similarity transformation technique to obtain these solutions. It turns out that the generalized nonautonomous NLSE with space-dependent coefficients can be reduced to the stationary NLSE, provided certain constraints are placed on the linear and nonlinear refractive indices. Various shapes of exact vortex soliton solutions are studied theoretically and analytically. Finally, the stability analysis of the solutions is discussed numerically. Our findings address an alternative way for the realization of stable vortex solitons with higher topological charges and the radial quantum numbers.

Vector vortex solitons in two-component Bose–Einstein condensates with modulated nonlinearities and a harmonic trap

Abstract We introduce vector solitary waves in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and a harmonic trapping potential. Using the self-similarity method, novel vector solitary waves are built with the help of Whittaker function, including multipole solutions and necklace rings. The stability of vortex soliton pairs is examined by direct numerical simulation; the results show that a new class of stable low-order vortex soliton pairs with n = 2 and m ≤ 3 can be supported by the spatially modulated interaction in the harmonic trap. Higher order vector-vortex soliton is found unstable over prolonged distances.