相关论文: Talbot Effect for the Manakov System on the Torus

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…

Consider continuous-time linear switched systems on R^n associated with compact convex sets of matrices. When the system is irreducible and the largest Lyapunov exponent is equal to zero, there always exists a Barabanov norm (i.e. a norm…

In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…

This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…

In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the difference of the nonlinear and the linear…

It is well known from results of Sina\u{\i} and Bowen that a hyperbolic toral automorphism admits a Markov partition. Our aim is to generalize this concept to the nonstationary case, i.e., we associate Markov partitions to nonstationary…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…

This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D)…

We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial…

We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…

We consider weak solutions to dispersive partial differential equations with periodic boundary conditions and initial data with jump discontinuities. These are already known to be continuous at irrational times and piecewise constant at…

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…

The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type…

This paper starts by an investigation of nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting a rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well…

Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…

We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…

We study higher-order modulation instability phenomena in the frame of Manakov equations. Evolution that starts with a single pair of sidebands expands over several higher harmonics. The choice of initial pair of sidebands influences the…