Solitons and Fractal Kerr Response

Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized.     

饱和光纤中的各阶孤子及孤子相互作用

首先研究了非线性饱和光纤中各阶孤子存在的幅值范围，与标准非饱和情况的非线性薛定谔孤子非常不同，即一阶孤子幅值范围是１．４≤Ｎ≤∵．０，二阶孤子为４．０≤Ｎ≤♀．０，三阶孤子为７．０≤Ｎ≤≤１５．０，并分析了各阶孤子的传输特性，最后研究了双一阶孤子相作用的若干特点，明确了五个方面的特性。     

Dark Multi-Soliton Solution of the Nonlinear Schrödinger Equation with Non-Vanishing Boundary

The inverse scattering transform for the nonlinear Schrödinger equation in normal dispersion with non-vanishing boundary values is re-examined using an affine parameter to avoid double-valued functions. An operable algebraic procedure is developed to evaluate dark multi-soliton solutions. The dark two-soliton solution is given explicitly as an example, and is verified by direct substitution. The additional motion of the soliton center is given by its asymptotic behavior.     

Thomson scattering induced by gravitational waves

We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically, as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization.     

String behaviour of magnetic field lines and their rotation in neutron star’s interior

It is found from Maxwell’s equations that the magnetic field lines are good analogues of relativistic strings. The Lorentz force per unit length of magnetic tube is interpretable as Magnus force acting on each individual magnetic tube. It is shown that the superconducting current in pulsar’s interior causes local rotation of magnetic flux tubes carrying quantized flux. Such local rotation remains operative as long as the induced magnetic field of normal electron fluid is above the lower critical field but below the upper. The conservation of magnetic flux leads to a geometrical condition in the form of the Weingarten identity which ensures the existence of family of “magnetic world sheetrdquo;. Each “magnetic world sheet” is a magnetic flux conserving surface. In the process of collapse, a compact spacelike cross-section of a magnetic tube terminates into a trapped surface if the magnetic energy grows faster along the fluid flow lines than that along the magnetic field lines.     

General Solution for Hamiltonians with Extended Cubic and Quartic Potentials

In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases 1:6:1 and 1:6:8.     

Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode

We investigate the dynamics of the wave packet formed by two codirected strongly interacting waves propagating in a medium with cubic nonlinearity. We obtain a soliton solution of the nonlinear Schrödinger equation in the degenerate case where the wave packet is described by a single partial momentum. In the nondegenerate case, we use the variational method to find the equation for the pulse duration, which turns out to be analogous to the equation for the coordinate in the Kepler problem. Solving it, we find the dependences of the pulse duration on the propagation distance in the cases of finite and infinite propagation regimes.     

Parametric Transducers for the Advanced Cryogenic Resonant-Mass Gravitational Wave Detectors

It is shown that a large improvement in liquid helium and ultra-cryogenically cooled resonant-mass gravitational wave detectors can be achieved through improved parametric transducers using either low loss sapphire dielectric resonators or niobium re-entrant cavities. Performance is analysed in relation to the existing resonant bar antenna Niobe and to massive spherical detectors. Applied to Niobe, a millisecond burst sensitivity of order 10^–20 can be achieved, corresponding to a spectral strain sensitivity of 2 × 10^-22 Hz with a 50 Hz bandwidth. Applied to an ultra-cryogenic 117 tonne spherical detector made from CuAl, a spectral strain sensitivity of better than 2 ×10^-23/ Hz with a bandwidth of order 100 Hz can be achieved, which is close to the quantum limit. This sensitivity is comparable to that of advanced interferometer detectors at this frequency.     

Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach

Higher-order corrections of the Einstein–Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where the Ricci scalar R and its d'Alembertian R are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify the dynamics by recovering constants of motion. The main result is that a Noether vector seems to rule the presence of higher-order corrections of gravity.     

用三角函数法获得非线性Boussinesq方程的广义孤子解

找到一个合适的代换——三角函数法，将非线性Boussinesq微分方程转换为非线性代数方程组.用吴消元法求解该非线性代数方程组，从而获得一般形式Boussinesq微分方程的广义孤子解. 关键词： Boussinesq方程 吴消元法 非线性代数方程组 孤子解