相关论文: Nonlinear stability of Gardner breathers

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to…

On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by…

We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the expansion of the nonlinearity. All terms may be computed…

We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…

Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse are shown to be globally $H^1$-stable. Stability in the one-kink case was previously established by Zhidkov, and Merle-Vega. The proof uses…

In this note, we review stability properties in energy spaces of three important nonlinear Schr\"odinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard…

The infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (NLS) equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a…

We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…

The paper addresses compact oscillatory states (compact breathers) in translationally-invariant lattices with flat dispersion bands. The compact breathers appear in such systems even in the linear approximation. If the interactions are…

The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…

We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some…

Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and…

Using two methods we show that a quantized discrete breather in a 1-D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as…

We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinear stability of steady states which are decreasing functions…

Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling-wave solutions of viscous systems of conservation laws for systems of…

We prove the nonlinear stability of the KdV solitary waves considered as solutions of the KP-II equation, with respect to periodic transverse perturbations.

We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibrium model is scalar, under the necessary assumption of…

We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By…

We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with…

We study the thermal equilibrium of nonlinear Klein-Gordon chains at the limit of small coupling (anticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the…