相关论文: Nonlinear localized waves in a periodic medium
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
The modulational instability and discrete matter wave solitons in dipolar BEC, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a…
Inspired by [25], this paper investigates subwavelength bandgaps in phononic crystals consisting of periodically arranged hard elastic materials embedded in a soft elastic background medium. Our contributions are threefold. First, we…
The thermomagnetic instability of the critical state in superconductors is analysed with account of the dissipation and dispersion. The possibility is demonstrated of the existance of a nonlinear shok wave describing the final stage of the…
In this paper we study a system of coupled nonlinear Schrodinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and…
Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. The…
We show that nonlinear imaging is possible in periodic waveguide configurations provided that we use two different segments of nonlinear media with opposite signs of the Kerr nonlinearity with, in general, no other restriction about their…
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.
In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive.…
We consider the quadratic and cubic KP - I and NLS models in $1+2$ dimensions with periodic boundary conditions. We show that the spatially periodic travelling waves (with period $K$) in the form $u(t,x,y)=\vp(x-c t)$ are spectrally and…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…
Density-wave patterns in (quasi-) discrete media with local interactions are known to be unstable. We demonstrate that \emph{stable} double- and triple- period patterns (DPPs and TPPs), with respect to the period of the underlying lattice,…
Parametric modeling of non-stationary signals is addressed in this article. We present several models based on the characteristic features of the modeled signal, together with the methods for accurate estimation of model parameters.…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
We review the properties of nonlinear, multidimensional localized waves whose stationary propagation is sustained by a dynamic equilibrium between self-focusing and nonlinear losses. Their finite-energy versions preserve light bullet…
We investigate Fano-type anomalous transmission of energy of plane waves across lossless slab scatterers with periodic structure in the presence of non-robust guided modes. Our approach is based on rigorous analytic perturbation of the…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…