槽中双孤子互作用的微扰求解

孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态 关键词： Miles方程 微扰双孤子解     

BaTiO3晶体中光束自陷的理论研究

对聚焦光束通过有一定外加电场ＢａＴｉＯ３晶体时的自陷现象进行了理论分析，发现在正切割晶体中观察空间孤子是不合适的，因仅利用了很微小的电光系数γ３３。对异型切割情况进行了讨论，给出了维持光束自陷的外加电场范围和实际观察的最佳角度。     

强非局域非线性介质中光束传输的空间光孤子解

利用1+2维Snyder-Mitchell模型讨论了柱坐标系下光束传输过程，得到了强非局域非线性介质中光束稳定传输的拉盖尔高斯型解，即空间光孤子解，并得到了入射光束稳定传输的临界功率.图示展现了几个低阶光孤子解，并发现了强非局域非线性介质中存在圆环形光孤子. 关键词： 强非局域非线性介质 拉盖尔高斯(Laguerre-Gauss)解 高阶空间光孤子     

Non-linear polarization and chiral effects in birefringent solitons

Novel effects resulting from joint action of chirality and non-linearity are discussed using a basic equation describing the temporal evolution of fields in a chiral medium with Kerr non-linearity. The spatial chirality effect is characterized through the Born-Fedorov formalism. Our simulations are based on the split-step Fourier method and the solution of the Stokes parameters. The numerical results show the chiral effect on solitons with circular polarization and mixed polarization spatial solitons.     

离散的五次非线性薛定谔方程的精确孤子解

利用推广的双曲函数法，我们研究了离散的五次非线性薛定谔方程。当方程的系数满足某种约束关系时，我们得到了新的局域解。这些解包括亮孤子解，暗孤子解，相位交替变化的亮孤子解和相位交替变化的暗孤子解。     

Wave Regimes of Viscous Film Flow down a Vertical Cylinder

The flow of a viscous liquid film down a vertical cylinder in the gravity field is considered. In the case of small Reynolds numbers for long-wave perturbations on a cylinder of radius much greater than the film thickness, the problem can be reduced to a single nonlinear equation for the evolution of the film thickness perturbation. For axially symmetric solutions, this equation coincides with the well-known Sivashinsky-Kuramoto equation. The results of a numerical analysis of this equation for three-dimensional stationary traveling solutions of the problem are reported. The effect of the problem parameters on the solution behavior is demonstrated. Soliton type solutions are presented.     

Optical filaments and optical bullets in dispersive nonlinear media

We have investigated the evolution of picosecond and femtosecond optical pulses governed by the amplitude vector equation in the optical and UV domains. We have written this equation in different coordinate frames, namely, in the laboratory frame, the Galilean frame, and the moving-in-time frame and have normalized it for the cases of different and equal transverse and longitudinal sizes of optical pulses or modulated optical waves. For optical pulses with a small transverse size and a large longitudinal size (optical filaments), we obtain the well-known paraxial approximation in all the coordinate frames, while for optical pulses with relatively equal transverse and longitudinal sizes (so-called light bullets), we obtain new non-paraxial nonlinear amplitude equations. In the case of optical fields with low intensity, we have reduced the nonlinear amplitude vector equations governing the light-bullet evolution to the linear amplitude equations. We have solved the linear equations using the method of Fourier transform. An unexpected new result is the relative stability of light bullets and the significant decrease in the diffraction enlargement of light bullets with respect to the case of long pulses in the linear propagation regime.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.     

Mott transition in anharmonic confinement

Two effects are identified that affect the visibility of the Mott transition in an atomic gas in an optical lattice confined in a power-law potential. The transition can be made more pronounced by increasing the power law, but at the same time, experimental uncertainty in the number of particles will induce corresponding fluctuations in the measured condensate fraction. Calculations in two dimensions indicate that a potential slightly more flat-bottomed than a quadratic one is to be preferred for a wide range of particle number fluctuation size.