Related papers: An analytical connection between temporal and spat…
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against…
We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is…
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…
We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly…
In this paper, we analyse the dynamics of a pattern-forming system close to simultaneous Turing and Turing--Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a…
Global and local absolute instabilities of 2D wakes are known to be stabilized by spanwise periodic modulations of the wake profile. The present study shows that this stabilizing effect is of general nature and can be mimicked by enforcing…
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
We revisit the nonlinear stability of the critical invasion front in the Ginzburg-Landau equation. Our main result shows that the amplitude of localized perturbations decays with rate $t^{-3/2}$, while the phase decays diffusively. We…
In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
To predict allowable time-step size for the fully discretized nonlinear differential equations, a stability theory is developed using exact determination of an infinite perturbation series. Mathematical induction is used to determine the…
This paper focuses on providing the high order algorithms for the space-time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being…
Motivated by recent experiments, the theoretical study of wave propagation in time varying materials is of current interest. Although significant in nearly all such experiments, material dispersion is commonly neglected in theoretical…
We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…
For the complex Ginzburg-Landau equation on a large periodic interval, we show that the transition from defect- to phase-turbulence is more accurately described as a smooth crossover rather than as a sharp continuous transition. We obtain…