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We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…
A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…
We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show this is modeled by a nonlinear diffraction term in a nonlinear schroedinger type equation, in which the…
We construct and simulate the dynamics of gauged vortons - circular loops of cosmic string supported by the angular momentum of trapped charge and current and provide additional details on the fully stable vorton that we have previously…
In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the…
The stability of large-scale magnetic fields in rotating stars is explored, using 3D numerical hydrodynamics to follow the evolution of an initial poloidal field. It is found that the field is subject to an instability, located initially on…
The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
The formation of patterns in driven systems has been studied extensively, and their emergence can be connected to a fine balance of instabilities and stabilization mechanisms. While the early phase of pattern formation can be understood on…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago,…
We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of the time derivatives of slow and fast variables is of order $0<\eps \ll 1$. At frozen…
We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…
We investigate the radial stability of neutron stars under conditions where their composition may or may not remain in chemical equilibrium during oscillations. Using different equations of state that include nucleons, hyperons, and/or…