Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing

I=2 Pion scattering length with improved actions on anisotropic lattices

$\pi\pi$ scattering length in the I=2 channel is calculated within quenched approximation using improved gauge and improved Wilson fermion actions on anisotropic lattices. The results are extrapolated towards the chiral, infinite volume and continuum limit. This result improves our previous result on the scattering length. In the chiral, infinite volume and continuum limit, we obtain $a^{(2)}_0m_\pi=-0.0467(45)$, which is consistent with the result from Chiral Perturbation Theory, the experiment and results from other lattice calculations.Comment: 7 pages, 2 figures, typeset wit elsart.cl

The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination system for polynomial, the classifications of all single traveling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More general, an implicit linear structure in Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion

Rayleigh lidar observations of gravity wave activity in the stratosphere and lower mesosphere

Forty-two monochromatic gravity wave events were observed in the 25 to 55 km altitude region during 16 nights of Rayleigh lidar measurements at Poker Flat, Alaska and Urbana, Illinois. The measured wave parameters were compared to previous radar and lidar measurements of gravity wave activity. Vertical wavelengths, lambda(z), between 2 and 11.5 km with vertical phase velocities, c(z), between 0.1 and 1 m/s were observed. Measured values of lambda(z) and c(z) were used to infer observed wave periods, T(ob), between 50 and 1000 minutes and horizontal wavelengths, lambda(x), from 25 to 2000 km. Dominant wave activity was found at vertical wavelengths between 2 to 4 km and 7 to 10 km. No seasonal variations were evident in the observed wave parameters. Vertical and horizontal wavelengths showed a clear tendency to increase with T(ob), which is consistent with recent sodium lidar studies of monochromatic wave events near the mesopause. Measured power law relationships between the wave parameters were lambda(z) varies as T(ob) sup 0.96, lambda(x) varies as T(ob) sup 1.8, and c(z) varies as T(ob) sup -0.85. The kinetic energy calculated for the monochromatic wave events varied as k(z) sup -2, k(x) sup -1, and f(ob) sup -1.7. The atmospheric scale heights calculated for each observation date range from 6.5 to 7.6 km with a mean value of 7 km. The increase of rms wind perturbations with altitude indicated an amplitude growth length of 20.9 km. The altitude profile of kinetic energy density decreased with height, suggesting that waves in this altitude region were subject to dissipation or saturation effects

Rayleigh lidar observations of gravity wave activity in the upper stratosphere at Urbana, Ill.

During 13 nights of Rayleigh lidar measurements at Urbana, Ill. in 1984 to 1986, thirty-six quasi-monochromatic gravity waves were observed in the 35 to 50 km altitude region of the stratosphere. The characteristics of the waves are compared with other lidar and radar measurements of gravity waves and the theoretical models of wave saturation and dissipation phenomena. The measured vertical wavelengths ranged from 2 to 11.5 km and the measured vertical phase velocities ranged from 10 to 85 cm/s. The vertical wavelengths and vertical phase velocities were used to infer observed wave periods which ranged from 100 to 1000 min and horizontal wavelengths which ranged from 70 to 2000 km. Dominant wave activity was found at vertical wavelengths between 2 to 4 km and 7 to 10 km. No significant seasonal variations were evident in the observed parameters. Vertical and horizontal wavelengths showed a clear tendency to increase with wave periods, which is consistent with recent sodium lidar studies of quasi-monochromatic waves near the mesopause. An average amplitude growth length of 20.9 km for the rms wind perturbations was estimated from the data. Kinetic energy density associated with the waves decreased with height, suggesting that waves in this altitude region were subject to dissipation or saturation effects

The nature of the KFR08 stellar stream

The origin of a new kinematically identified metal-poor stellar stream, the KFR08 stream, has not been established. We present stellar parameters, stellar ages, and detailed elemental abundances for Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Ni, Zn, Sr, Y, Zr, Ba, La, and Eu for 16 KFR08 stream members based on analysis of high resolution spectra. Based on the abundance ratios of 14 elements, we use the chemical tagging method to identify the stars which have the same chemical composition, and thus, might have a common birthplace, such as a cluster. Although three stars were tagged with similar elemental abundances ratios, we find that, statistically, it is not certain that they originate from a dissolved star cluster. This conclusion is consistent with the large dispersion of [Fe/H] ($\sigma_{\rm{[Fe/H]}} = 0.29$) among the 16 stream members. We find that our stars are $\alpha$ enhanced and that the abundance patterns of the stream members are well matched to the thick disk. In addition, most of the stream stars have estimated stellar ages larger than 11 Gyr. These results, together with the hot kinematics of the stream stars, suggest that the KFR08 stream is originated from the thick disk population which was perturbed by a massive merger in the early universe.Comment: 9 pages, 6 figures, accepted for publication in A&