Pseudospin solitons in the coherent stripe phase of a bilayer quantum Hall system

In the Hartree–Fock approximation and at total filling factor ν=4N+1, the ground state of the two-dimensional electron gas in a double quantum well system in a quantizing magnetic field is, in some range of interlayer distances, a coherent striped phase. This stripe phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton–antisoliton pairs using a supercell microscopic unrestricted Hartree–Fock approach. We study the energy gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton–antisoliton excitation energy is lower than the corresponding Hartree–Fock electron–hole pair energy.     

Stochastic perturbation of non-Kerr law optical solitons

The dynamics of optical solitons with non-Kerr law non-linearities, in presence of stochastic perturbation terms, is studied in this paper. The Langevin equations are derived and it is proved that the solitons travel through a fiber with a fixed mean velocity. The non-linearities that are considered here are the power law, parabolic law and the dual-power law types.     

On the extended KdV equation with self-consistent sources

The positive extended KdV equation with self-consistent sources (eKdV⁺ ESCSs) is firstly presented and its related linear auxiliary equation is derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV⁺ ESCSs such as N-soliton solution, N-double pole solution and nonsingular N-positon solution. The properties of these solutions are analyzed. Moreover, the interaction of two solitons is discussed in detail.     

All-Optical Logic Device Using Bent Nonlinear Tapered Y-Junction Waveguide Structure

We propose an all-optical logic device made of a bent tapered Y-junction waveguide with a Kerr-type nonlinear interface. It could provide an AND gate, OR gate, and exclusive-OR (XOR) gate. We could obtain different transmission results by adjusting the bending angle. The numerical simulation results show that the device functions as AND, OR, and XOR gates.     

生物能量传递新模型中的孤立子特性研究

从庞提出的新的生物能量传递理论出发,用Runge-Kutta方法和蛋白质分子的特征参数值对该理论的基本动力学方程进行了数值模拟,求出了孤立子在自由运动下、在相互碰撞时以及它在长时间运动后的特征.研究表明,在这些运动过程中,这个孤立子始终保持稳定状态.于是看到它能真正承担起在蛋白质分子传递生物能量的功能.从而从数值模拟的角度证明了新理论的可利用性.     

Interaction of multi-lumps within the Kadomtsev–Petviashvili equation

The interactions of multi-lumps within the Kadomtsev–Petviashvili-1 (KP1) equation are studied analytically and numerically. The dependence of stationary multi-lump structures on free parameters is discussed. The interactions of single lumps with each other and with a more complex objects such as bi-lumps, as well as the interactions of bi-lumps with each other are studied numerically. The results obtained are described and illustrated graphically (the videos are also available).     

Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structures. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a sine–Gordon type equation which is known to have soliton solutions.     

Asymptotics and Blow-up for Mass Critical Nonlinear Dispersive Equations

The author considers mass critical nonlinear Schr（o）dinger and Korteweg-de Vries equations.A review on results related to the blow-up of solution of these equations is given.     

Other incarnations of the Gross-Pitaevskii dark soliton

We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. As a consequence of this, the GPE soliton gets related to the magnetic soliton in an easy-plane ferromagnet, where it describes the square of the in-plane magnetization of the system. These relationships are shown to be useful in understanding various characteristics of solitons in these distinct many-body systems.