Related papers: The stability of the scalar $\chi^2\phi$ interacti…
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation $\Delta^2 \phi = \phi^p$. First, we show that there exists a critical value $p_c$, depending on the space dimension, such that the solutions…
We show that the potential of the scalar field in the Einstein frame is flat if the nonminimal coupling term is properly chosen that it satisfies the condition (V(phi)/K^2(phi)-> constant) as phi gets large. The cosmological implication of…
We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called…
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…
The present work is an extensive study of the viable stable solutions of chameleon scalar field models leading to possibilities of an accelerated expansion of the universe. It is found that for various combinations of the chameleon field…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
A system of gluon fields generated at the earliest phase of relativistic heavy-ion collisions can be described in terms of classical fields. Numerical simulations show that the system is unstable but a character of the instability is not…
The stability of scalar quintessence potentials under quantum fluctuations is investigated both for uncoupled models and models with a coupling to fermions. We find that uncoupled models are usually stable in the late universe. However, a…
We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable…
We investigate the stability of an Fermi ball(F-ball) within the next-to-leading order approximation in the thin wall expansion. We find out that an F-ball is unstable in case that it is electrically neutral. We then find out that an…
A polynomial $f(x)$ over a field $K$ is called stable if all of its iterates are irreducible over $K$. In this paper we study the stability of trinomials over finite fields. Specially, we show that if $f(x)$ is a trinomial of even degree…
The stability of scalar quintessence potentials under quantum fluctuations is investigated for both uncoupled models and models with a coupling to fermions. We find that uncoupled models are usually stable in the late universe. However, the…
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of…
We consider the general higher derivative field theories of derived type. At free level, the wave operator of derived-type theory is a polynomial of the order $n\geq 2$ of another operator $W$ which is of the lower order. Every symmetry of…
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $\chi$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptotically stable, but by using a technique inspired by H. Fujita, we…
We revisit the dynamics of a nonminimally coupled scalar field model in case of $F(\phi)R$ coupling with $F(\phi)= 1-\xi\phi^2 $, and the potentials $V(\phi) = V_0 (1+ \phi^p)^2$, $V(\phi)= V_0 e^{\lambda \phi^2}$. We use an autonomous…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
We study the model of a massive inflaton field $\phi$ coupled to another scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$ for the first stage of preheating. We obtain the the behavior of the phase in terms of the iteration of a…