相关论文: Amplitude equations and pattern selection in Farad…

The Faraday wave experiment is a classic example of a system driven by parametric forcing, and it produces a wide range of complex patterns, including superlattice patterns and quasipatterns. Nonlinear three-wave interactions between driven…

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…

We propose that parametrically excited patterns, also known as Faraday patterns, can be observed in nonlinear fiber resonators, where the coefficient of Kerr nonlinearity is periodically varying along the fiber in resonator. We study the…

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit…

The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a…

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…

A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…

Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…

It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…

We report on surface wave pattern formation in a Faraday experiment operated at a very shallow filling level, where modes with a subharmonic and harmonic time dependence interact. Associated with this distinct temporal behavior are…

Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…

Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…

Parametrically excited standing waves are observed on a cylindrical fluid filament. These are the cylindrical analog of Faraday instability in a flat surface or spherical droplet. Using the Floquet technique, linear stability analysis has…

The first part of the paper proves that a subset of the general set of Ermakov-Pinney equations can be obtained by differentiation of a first-order non-linear differential equation. The second part of the paper proves that, similarly, the…

We make rigorous spectral stability analysis for non-resonant capillary-gravity waves as well as resonant Wilton ripples of sufficiently small amplitude. Our analysis is based on a periodic Evans function approach, developed recently by the…

A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…

We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents in the…