相关论文: Existence and stability of periodic planar standin…

We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…

We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.

The comprehensive investigation of the temporal evolution of the diocotron instability of the plane electron strip on the linear stage of its development is performed. By using the Kelvin's method of the shearing modes we elucidate the role…

We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1+1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are…

We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…

It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not…

In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schr\"odinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained…

We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…

In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…

We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…

This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or…

As presented in Annenkov & Shrira (2009), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ``fast'' dynamic time scale of $O(\varepsilon^{-2})$, with $\varepsilon$ a…

In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schr\"odinger equations with potentials. We show that the standing waves are orbitally stable for all frequencies in the $L^{2}$- subcritical and…

We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…

We study motion of a phase transition front at a constant temperature between stable and metastable states in fluids with the universal Van der Waals equation of state (which is valid sufficiently close to the fluid's critical point). We…

Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes…

We report on the growth of domains of standing waves in electroconvection in a nematic liquid crystal. An ac voltage is applied to the system, forming an initial state that consists of travelling striped patterns with two different…

We study the following family of evolutionary 1+1 PDEs that describe the balance between convection and stretching for small viscosity in the dynamics of 1D nonlinear waves in fluids: \[ m_t + \underbrace{um_x \}…

We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr\"{o}dinger equation with the same type of the nonlinearity. The model opens a way to study the…

We study the stability of a four parameter family of spatially periodic traveling wave solutions of the generalized Benjamin-Bona-Mahony equation to two classes of perturbations: periodic perturbations with the same periodic structure as…