Related papers: On a hypercycle equation with infinitely many memb…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
The existence of travelling waves for a coupled system of hyperbolic/ parabolic equations is established in the case of a finite number of velocities in the kinetic equation. This finds application in collective motion of chemotactic…
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple…
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions on the linearised operator. Perturbations are moreover…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
We prove a Liv\v{s}ic-type theorem for H\"older continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever $(f,\mu)$ is a non-uniformly hyperbolic system and $A:M \to GL(d,\mathbb{R})…
The dynamics of a molecule immersed in a superfluid medium are considered. Results are derived using a classical hydrodynamic approach followed by canonical quantization. The classical model, a rigid body immersed in incompressible fluid,…
Exponential dichotomy of a strongly continuous cocycle $\bFi$ is proved to be equivalent to existence of a Ma\~{n}e sequence either for $\bFi$ or for its adjoint. As a consequence we extend some of the classical results to general Banach…
Modular and quasimodular solutions of specific second order differential equation in the upper-half plane which originates from a study of supersingular j-invariants are given explicitly. A characterization of the differential equation is…
In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that,…
We consider a (mathbb{Z}_2)-equivariant flow in (mathbb{R}^{4}) with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit (Gamma). We provide criteria for the existence of stable and unstable invariant…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
An axisymmetric static solution of a nonlinear electrodynamics is considered as a massive charged particle with spin and magnetic moment. A linearization of the nonlinear electrodynamics around the static solution is investigated. The…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…