We study the long-time stability of soliton solutions to the Korteweg-deVries equation. We consider solutions u to the KdV with initial data in Hs, 0 ≤ s < 1, that are initially close in Hs norm to a soliton. We prove that the possible orbital instability of these ground states is at most polynomial in time. This is an analogue to the Hs orbital instability result of [7], and obtains the same m...

Two new effects of interaction of the gauge string with a homogeneous density of fermions are considered in a gauge model with an anomalous coupling of vector fields with fermions. First, the presence of an induced nonzero magnetic-like helicity on the straight string is demonstrated. Second, it is shown that the equation of motion of the string is modified by a nonlinear term that can be decom...

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown ...

We obtain the supergravity solution which describes a bound state of D-string/anti-D-string pairs attached to different fixed planes of an orbifold, in type IIB string theory compactified on T /Z2. For parameters at which the conformal field theory point of view predicts stability, the solution displays a repulson-like singularity. However, we observe that a D-string/anti-D-string pair probe in...

In this paper we study a one dimensional thermoelastic transmission problem of special string/beam structure: the two components are coupled at an interface (identified to $ 0 $). Either string or beam is supposed thermoelastic, heat flux given by Cattaneo's law instead usual Fourier's law. We prove that energy decay whole system exponential if thermoelastic. When only coupling decays polynomia...

Article history: Received 27 March 2017 Received in revised form 8 May 2017 Accepted 8 May 2017 Available online 10 May 2017 Editor: N. Lambert Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2 < d < 26. Recently we have showed that at large d there is another socalled mean-field vacuum. Here we extend this mean-field calcu...