相关论文: Multi-stable regime and intermediate solutions in …

Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain…

We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…

Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed:…

A generic photonic coupler with active and lossy parts, gain saturation and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to…

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an…

This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an…

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…

We study an intense-short pulse propagation in a saturable cubic-quintic nonlinear media in the presence of nonlinear dispersion within the framework of an extended variational approach. We derive an effective equation for the pulse width…

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…

We investigate the properties of nonlinear excitations in different types of soliton bearing systems with long-range dispersive interaction. We show that length-scale competition in such systems universally results in a multi-component…

We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…

We prove the existence of ground state in a multidimensional nonlinear Schrodinger model of paraxial beam propagation in isotropic local media with saturable nonlinearity. Such ground states exist in the form of bright counterpropagating…

Linear stability of stratified gas-liquid and liquid-liquid plane-parallel flows in inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict parameter regions in which stable stratified…

We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…

We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different…

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…