Instability of the solitary waves for the generalized Boussinesq equations

In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\mathbb R\times \mathbb R, \end{align*} with $0<p<\infty$. This equation has the traveling wave solutions $\phi_\omega(x-\omega t)$, with the frequency $\omega\in (-1,1)$ and $\phi_\omega$ satisfying \begin{align*} -\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0. \end{align*} Bona and Sachs (1988) proved that the traveling wave $\phi_\omega(x-\omega t)$ is orbitally stable when $0<p<4,$ $\frac p4<\omega^2<1$. Liu (1993) proved the orbital instability under the conditions $0<p<4,$ $\omega^2<\frac p4$ or $p\ge 4,$ $\omega^2<1$. In this paper, we prove the orbital instability in the degenerate case $0<p<4,\omega^2=\frac p4$ .Comment: 29 page

Effects of Rashba spin-orbit coupling and a magnetic field on a polygonal quantum ring

Using standard quantum network method, we analytically investigate the effect of Rashba spin-orbit coupling (RSOC) and a magnetic field on the spin transport properties of a polygonal quantum ring. Using Landauer-Buttiker formula, we have found that the polarization direction and phase of transmitted electrons can be controlled by both the magnetic field and RSOC. A device to generate a spin-polarized conductance in a polygon with an arbitrary number of sides is discussed. This device would permit precise control of spin and selectively provide spin filtering for either spin up or spin down simply by interchanging the source and drain

Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space

A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} = 0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the $95\%$ confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which $\alpha_\mathrm{s}$, $n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and $\Sigma m_\mathrm{\nu}$ are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on $r_\mathrm{0.002}$ are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that $N_\mathrm{eff}$ probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain $r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$, $n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and $\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.Comment: 8 pages, 4 figures, submitted to PL

Research on Influence Factors of the Internet Financial Product Consumption Based on Innovation Diffusion Theory

This article takes the personal characteristic as a point of penetration,through a literature review, put forwards three antecedents factors,that are personal innovation, product cognition and perceived risk, focusing on the relationship among the there factors,the conceptual model was tested by structural equation model .The findings are that all of the above three aspects influence the choice of the Internet financial products. They also mutual influence between the three, personal innovation has a positive impact on product cognition and gives a negative impact on perceived risk, at the same time, product cognition affects the perceived risk negatively