The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

It is proved, using a bootstrap argument, that linear instability implies nonlinear instability for the incompressible Navier-Stokes equations in L for all p ∈ (1,∞) and any finite or infinite domain in any dimension n.

Using WKB methods for very small times, we prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. The main step of the analysis consists in reducing the problem to an ordinary differential equation. The solution to this o.d.e. is explicit, and the instability mechanism is due to the presence of the semi-classical parameter. For nonlin-ear equations, our...

We present an investigation of the modulational instability of partially coherent signals in electrical transmission lines. Starting from the modified Ginzburg-Landau equations and the Wigner-Moyal representation, we derive a nonlinear dispersion relation for the modulational instability. It is found that the effect of signal broadbandness reduces the growth rate of the modulational instability.

In this article the instability of single phase flow in a circular pipe from laminar to turbulence regime has been investigated. To this end, after finding boundary conditions and equation related to instability of flow in cylindrical coordination system, which is called eigenvalue Orr Sommerfeld equation, the solution method for these equation has been investigated. In this article Chebyshev p...

This paper provides the first study of a new dynamical instability in superfluids. This instability is similar to the two-stream instability known to operate in plasmas. It is analogous to the Kelvin-Helmholtz instability, but has the distinguishing feature that the two fluids are interpenetrating. The instability sets in once the relative flow between the two components of the system reaches a...

Oscillations described by autonomous three-dimensional differential equations display multiple periodicities and chaos at critical parameter values. Regardless of the subsequent scenario the key instability is often an initial bifurcation from a single period oscillation to either its subharmonic of period two, or a symmetry breaking bifurcation. A generalized third-order nonlinear differential...

in this paper, nonlinear vibration and instability response of an embedded pipe conveying viscose fluid is investigated. the pipe is considered as a timoshenko beam embedded on an elastic foundation which is simulated by spring constant of the winkler-model and the shear constant of the pasternak-model. the external flow force, acting on the beam in the direction of the flexural displacement is...

Few recent generations of cosmologists have solved non-local newtonian equations of the gravitational instability in an expanding universe. In this approach pancaking is the predominant form of first collapsing objects. Relativistic counterparts of these equations contain the electric and magnetic parts of the Weyl tensor. In the linear theory the magnetic part is associated with gravitational ...

Context. To investigate the physical nature of the 'nucleated instability' of proto giant planets, the stability of layers in static, radiative gas spheres is analysed on the basis of Baker's standard one-zone model. Aims. It is shown that stability depends only upon the equations of state, the opacities and the local thermodynamic state in the layer. Stability and instability can therefore be ...