Related papers: The stability problem and special solutions for th…
The stability of the elliptic solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation is studied. The orbital stability of the cmKdV equation was established in [19] when the periodic orbits do not oscillate around…
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…
A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie…
We will address the problem of determining the existence and asymptotic stability of a non-trivial periodic orbit in dynamical systems described by polynomial vector fields. To this end, we will lean upon the celebrated results of Borg,…
In the case of symmetries with respect to n independent linear hyperplanes, the stability of the solution of the Logarithmic Minkowski problem on S^{n-1} is established.
In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Besides black holes and wormholes, a new class of geodesically complete solutions is identified. A monopole perturbation…
Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their properties…
In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations…
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics",…
We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Both charged and neutral cases are considered. The analysis of the solutions, through their geometrical properties,…
We study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of four-dimensional systems which may be Hamiltonian or not. Only one parameter is enough to treat these types of bifurcations in Hamiltonian systems but…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
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 the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…