A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

Sine-Gordon方程的截断系统的同宿轨道

研究ＳｉｎｅＧｏｒｄｏｎ方程的广义渐近惯性流形上的常微分方程组，证实了在一定参数条件下存在Ｗｉｇｇｉｎｓ［１］意义下的同宿轨道．计算表明，与Ｂｉｓｈｏｐ［２］用数值计算得到的ＳｉｎｅＧｏｒｄｏｎ方程产生混沌的参数值尚有差别，考虑到同宿出现参数值往往低于混沌出现参数值，故结果在定性上正确，而且改进了文［１］中的结果．

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.

Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion

The nonlinear dynamics of 1.6-mu m fs laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at 670 nm. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.

Transient population and polarization gratings induced by (1+1)-dimensional ultrashort dipole soliton

An ultrafast transient population grating induced by a (1+1)-dimensional, ultrashort dipole soliton is demonstrated by solving the full-wave Maxwell-Bloch equations. The number of lines and the period of the grating can be controlled by the beam waist and the area of the pulse. Of interest is that a polarization grating is produced. A coherent control scheme based on these phenomena can be contemplated as ultrafast transient grating techniques.

Evolutionary implications of multiple SINE insertions in an intronic region from diverse mammals

An analysis of the nuclear beta-fibrinogen intron 7 locus from 30 taxa representing 12 placental orders of mammals reveals the enriched occurrences of short interspersed clement (SINE) insertion events. Mammalian-wide interspersed repeats (MIRs) are present at orthologous sites of all examined species except those in the order Rodentia. The higher substitution rate in mouse and a rare MIR deletion from rat account for the absence of MIR in the rodents. A minimum of five lineage-specific SINE sequences are also found to have independently inserted into this intron in Carnivora, Artiodactyla and Lagomorpha. In the case of Carnivora, the unique amplification pattern of order-specific CAN SINE provides important evidence for the "pan-carnivore" hypothesis of this repeat element and reveals that the CAN SINE family may still be active today. Particularly interesting is the finding that all identified lineage-specific SINE elements show a strong tendency to insert within or in very close proximity to the preexisting MIRs for their efficient integrations, suggesting that the MIR clement is a hot spot for successive insertions of other SINEs. The unexpected MIR excision as a result of a random deletion in the rat intron locus and the non-random site targeting detected by this study indicate that SINEs actually have a greater insertional flexibility and regional specificity than had previously been recognized. Implications for SINE sequence evolution upon and following integration, as well as the fascinating interactions between retroposons and the host genomes are discussed.

Bead-probe complex capture a couple of SINE and LINE family from genomes of two closely related species of East Asian cyprinid directly using magnetic separation

Background: Short and long interspersed elements (SINEs and LINEs, respectively), two types of retroposons, are active in shaping the architecture of genomes and powerful tools for studies of phylogeny and population biology. Here we developed special protocol to apply biotin-streptavidin bead system into isolation of interspersed repeated sequences rapidly and efficiently, in which SINEs and LINEs were captured directly from digested genomic DNA by hybridization to bead-probe complex in solution instead of traditional strategy including genomic library construction and screening. Results: A new couple of SINEs and LINEs that shared an almost identical 3'tail was isolated and characterized in silver carp and bighead carp of two closely related species. These SINEs (34 members), designated HAmo SINE family, were little divergent in sequence and flanked by obvious TSD indicated that HAmo SINE was very young family. The copy numbers of this family was estimated to 2 x 10(5) and 1.7 x 10(5) per haploid genome by Real-Time qPCR, respectively. The LINEs, identified as the homologs of LINE2 in other fishes, had a conserved primary sequence and secondary structures of the 3'tail region that was almost identical to that of HAmo SINE. These evidences suggest that HAmo SINEs are active and amplified recently utilizing the enzymatic machinery for retroposition of HAmoL2 through the recognition of higher-order structures of the conserved 42-tail region. We analyzed the possible structures of HAmo SINE that lead to successful amplification in genome and then deduced that HAmo SINE, SmaI SINE and FokI SINE that were similar in sequence each other, were probably generated independently and created by LINE family within the same lineage of a LINE phylogeny in the genomes of different hosts. Conclusion: The presented results show the advantage of the novel method for retroposons isolation and a pair of young SINE family and its partner LINE family in two carp fishes, which strengthened the hypotheses containing the slippage model for initiation of reverse transcription, retropositional parasitism of SINEs on LINEs, the formation of the stem loop structure in 3'tail region of some SINEs and LINEs and the mechanism of template switching in generating new SINE family.

Quantum teleportation via a two-qubit Heisenberg XXZ chain - effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ, chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

The thermal entanglement in a two-qubit Heisenberg XXZ spin chain is investigated under an inhomogeneous magnetic field b. We show that the ground-state entanglement is independent of the interaction of z-component J(z). The thermal entanglement at the fixed temperature can be enhanced when J(z) increases. We strictly show that for any temperature T and J(z), the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field b(c) is independent of J(z). The critical magnetic field B-c increases with the increasing parallel to b parallel to but the maximum entanglement value that the system can arrive at becomes smaller.

SWAP operation in the two-qubit Heisenberg XXZ model: Effects of anisotropy and magnetic field

In this paper we study the SWAP operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter lambda within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.