We consider the stability of the two branches of non-extremal enhançon solutions. We argue that one would expect a transition between the two branches at some value of the non-extremality, which should manifest itself in some instability. We study small perturbations of these solutions, constructing a sufficiently general ansatz for linearised perturbations of the non-extremal solutions, and sh...

We exploit a generic instability in the integration of steady, sonic, near-isothermal flows to find the complete transition diagram for recombination fronts (for a model system of equations). The instability requires the integration of the flow equations for speeds between the isothermal and adiabatic sound speeds to be performed with particular care. As a result of this, the previous work of N...

The linear wave and baroclinic instability properties of various geostrophic models valid when the Rossby number is small are investigated. The models are the ‘‘L1’’ dynamics, the ‘‘geostrophic potential vorticity’’ equations, and the more familiar quasigeostrophic and planetary geostrophic equations. Multilayer shallow water equations are used as a control. The goal is to determine whether the...

Due to the nonlinearity of Euler--Poisson equations, it is possible that nonlinear Jeans instability may lead a faster density growing rate than in standard theory linearized instability, which motivates us study instability. The aim this article develop method proving for slightly equations expanding Newtonian universe. proofs rely on Fourier analysis. However, difficult generalize setting, an...

This paper deals with the attitude motion of a dual-spin spacecraft which consists of an asymmetric rigid platform and an asymmetric rigid rotor connected together by a flexible joint. The equations of motion represent a flexible multiple-degree-of-freedom gyroscopic system with periodic coefficients due to asymmetries. The equations are analyzed for possible resonances and associated instabili...

This paper is an analytical investigation of the transverse electron-proton (e-p) two-stream instability in a proton bunch propagating through a stationary electron background. The equations of motion, including the effect of damping, are derived for the centroids of the proton beam and the electron cloud. An approach is developed to solve the coupled linear centroid equations in the time domai...

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term ...

This special session focuses on the dynamic properties of fluids and nonlinear waves arsing in systems such as Euler equations, kinetic equations, nonlinear Schrodinger equations, nonlinear wave equations etc. The main aspects include the global well-posedness of solutions, existence, stability/instability and nearby local qualitative structures of special states etc. The theory and the methods...

The Weibel instability in the quantum plasma case is treated by means of a fluid-like (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due t...

We study the orbital stability and instability of single-spike bound states of critical semi-classical nonlinear Schrödinger equations (NLS) with linear and nonlinear lattices. These equations may model an inhomogeneous Bose-Einstein condensate and an optical beam in a nonlinear lattice. When the linear lattice is switched off, we derive the asymptotic expansion formulas and obtain necessary co...