The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one movi...The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.展开更多
Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of（2＋1）-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vort...Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of（2＋1）-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex solitons via the similarity transformation method. The distance modulation for the width, the diffraction, and the nonlinear response, strongly affects the form and the behavior of the self-similar vortex, and facilitates the efficient compression of optical waves. This approximate ring-vortex solitons can reflect the real properties of self-similar optical vortex beams during propagation under certain parameter window selection. Specific examples and figures are given to illustrate discussed features. The results obtained in this paper may have potential values for all-optical data-processing schemes and the design of beam compressors and amplifiers.展开更多
By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ-type three-level self-assembled quantum ...By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ-type three-level self-assembled quantum dots. It is found that this system can exhibit the transparency, and the width of the transparency window becomes wider with the increase of control light field. Interestingly, a weak probe light beam can form spatial weak-light dark solitons. When it propagates along the axial direction, the soliton will transform into a steady spatial weak-light ring dark soltion. In addition, the stability of two-dimensional spatial optical solitons is testified numerically.展开更多
An analytical expression of ampere’s force between two current rings in a compensated torsion balance is deduced here,the properties and stability of this force are discussed.The result of numerical estimation for ty...An analytical expression of ampere’s force between two current rings in a compensated torsion balance is deduced here,the properties and stability of this force are discussed.The result of numerical estimation for typical experimental parameters shows that the uncertainties of the force are smaller than 1×10^(-4) orders,which is very important for precise measurement of gravitational constant G.展开更多
In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco）...In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco） τ-projective module and study their properties. When r is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a（inco） semisimple ring and satisfies（inco） condition.展开更多
Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least...Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such展开更多
The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumferen...The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a 0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sincot is found.展开更多
We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equa...We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation.Compared with previous results,the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling.With the modulation of the spin–orbit coupling,not only the lifetime of ring dark solitons is greatly prolonged,but also their attenuation kinetics is significantly affected.For two shallow ring dark solitons with the equal strength of the spin–orbit coupling,the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value.Due to the effect of the snake instability,ring dark solitons split into a series of ring-like clusters of vortex pairs,which perform complex oscillations.This indicates that the system is strongly dependent on the presence of the spin–orbit coupling.Furthermore,the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.展开更多
This paper addresses the ring-cavity fiber laser system. A class of gray and black soliton solutions of the model are reported by adopting an appropriate envelope ansatz. Further more, the modulation instability (MI) ...This paper addresses the ring-cavity fiber laser system. A class of gray and black soliton solutions of the model are reported by adopting an appropriate envelope ansatz. Further more, the modulation instability (MI) of the equation is studied using the linear-stability analysis (LSA) technique and the MI gain spectrum is derived. Some physical interpretations and analysis of the results obtained are also presented.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10347006 and 10475066）, and by the Natural Science Foundation of Gansu province （Grant No 3ZS051-A25-013）.
文摘The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.
文摘Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of（2＋1）-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex solitons via the similarity transformation method. The distance modulation for the width, the diffraction, and the nonlinear response, strongly affects the form and the behavior of the self-similar vortex, and facilitates the efficient compression of optical waves. This approximate ring-vortex solitons can reflect the real properties of self-similar optical vortex beams during propagation under certain parameter window selection. Specific examples and figures are given to illustrate discussed features. The results obtained in this paper may have potential values for all-optical data-processing schemes and the design of beam compressors and amplifiers.
基金Project supported by the Special Funds of the National Natural Science Foundation of China(Grant No.11247313)
文摘By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ-type three-level self-assembled quantum dots. It is found that this system can exhibit the transparency, and the width of the transparency window becomes wider with the increase of control light field. Interestingly, a weak probe light beam can form spatial weak-light dark solitons. When it propagates along the axial direction, the soliton will transform into a steady spatial weak-light ring dark soltion. In addition, the stability of two-dimensional spatial optical solitons is testified numerically.
文摘An analytical expression of ampere’s force between two current rings in a compensated torsion balance is deduced here,the properties and stability of this force are discussed.The result of numerical estimation for typical experimental parameters shows that the uncertainties of the force are smaller than 1×10^(-4) orders,which is very important for precise measurement of gravitational constant G.
基金Supported by the Science and Technology Develop Foundation of Jilin Science and Technology Department(20040506-3)
文摘In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco） τ-projective module and study their properties. When r is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a（inco） semisimple ring and satisfies（inco） condition.
文摘Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such
基金Project supported by Natural Science Foundation of Guangdong Province
文摘The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a 0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sincot is found.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LR20A050001)the National Natural Science Foundation of China(Grant Nos.12075210 and 12175129)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009).
文摘We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation.Compared with previous results,the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling.With the modulation of the spin–orbit coupling,not only the lifetime of ring dark solitons is greatly prolonged,but also their attenuation kinetics is significantly affected.For two shallow ring dark solitons with the equal strength of the spin–orbit coupling,the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value.Due to the effect of the snake instability,ring dark solitons split into a series of ring-like clusters of vortex pairs,which perform complex oscillations.This indicates that the system is strongly dependent on the presence of the spin–orbit coupling.Furthermore,the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.
文摘This paper addresses the ring-cavity fiber laser system. A class of gray and black soliton solutions of the model are reported by adopting an appropriate envelope ansatz. Further more, the modulation instability (MI) of the equation is studied using the linear-stability analysis (LSA) technique and the MI gain spectrum is derived. Some physical interpretations and analysis of the results obtained are also presented.
