Related papers: Steady states in dual-cascade wave turbulence
In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schr\"odinger-Kirchhoff equation. The presence of a mixed term gives us more dispersion, and consequently, a different scenario…
We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirected networks of nonlinear dynamical systems, when we consider…
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are…
We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov--Zakharov (KZ) spectrum in weak 3-wave turbulence. In the finite capacity case, in which the transient spectrum reaches infinite…
There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the…
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients.…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
The hypersonic flow stability over a two-dimensional compression corner is studied using resolvent analysis, linear stability theory (LST) and parabolised stability equation (PSE). The authors find that the interaction between upstream…
Recent work on the dynamics of a crystal surface [T.Frisch and A.Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved Kuramoto-Sivashinsky (CKS) equation: \partial_t u = -\partial_{xx}(u+u_{xx}+u_x^2), which…
We consider a non-linear, one-dimensional wave equation system with finite-dimensional stochastic driving terms and with weak dissipation. A stationary process that solves the system is used to model steady-state non-equilibrium heat flow…
We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kink-wise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires…
Different dynamics, described by kinetic equation and clipping method is shown as well as a role of approximate resonances in wave turbulence theory. Applications of clipping method are sketched for gravity-capillary and drift waves. Brief…
Wide channel Couette (WCC) turbulence is striking in being dominated by a large-scale spanwise periodic structure composed of streamwise streaks and associated roll superstructures. This apparent equilibrium is shown in this work to…