Related papers: Instability of pole singularities for the Chazy eq…
The dynamics of the oscillator system is investigated. The conditions under which this dynamics becomes unstable are determined. In particular, it is shown that plasma in constant magnetic field becomes unstable if its density exceeds a…
We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the…
Let $A$ be a (not necessarily unital) separable non-elementary simple amenable C*-algebra whose tracial basis may not have finite covering dimension and may not be compact but satisfies certain condition (C). We show that $A$ is ${\cal…
In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at…
Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
Magnetic fields vary in complexity for different stars. The stability of dipolar magnetic fields is known to depend on different quantities, e.g., the stellar rotation, the stratification, and the intensity of convective motions. Here, we…
In this work, we consider the generalized Benjamin-Bona-Mahony equation $$\partial_t u+\partial_x u+\partial_x( |u|^pu)-\partial_t \partial_x^{2}u=0, \quad(t,x) \in \mathbb{R} \times \mathbb{R}, $$ with $p>4$. This equation has the…
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the…
Bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using…
We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are…
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…
We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…
The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that…
The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…
The Cauchy problem in $\mathbb R^n$ is considered for \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v),\\ 0 = \Delta v + u. \end{array} \right. \end{eqnarray*} For each $n\ge 10$, a statement on stability…
We discuss the stability properties of the solutions of the general nonlinear \Schrodinger\ equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time ($\PT$) symmetric superpotential $W(x)$ that we considered…
This paper demonstrates some connections between the coefficients of a Taylor series $f(z)=\ds\sum_{n=0}^\infty a_n z^n$ and singularities of the function. There are many known results of this type, for example, counting the number of poles…
We review the evidence for and against the possibility that a strong enough poloidal field stabilizes an axisymmetric magnetostatic field configuration. We show that there does exist a class of resonant MHD waves which produce instability…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…